You may see that there is a dog in Chiro Caves who needs your help. You might search for a long time through all the tunnels but eventually you may find Henry in Chiro Caves B3.
Entrance of the Cave
Henry will tell you that he wants to get to the West Chilly Field, but the gate is closed. He then shows you the four pillars surrounding a pool of water with an Alligator in it. He tells you that if you were to put a Heavy Stone of each of the four pillars, the gate would open. He then tells you that you could probably find some Heavy Stones in the Chiro Caves, but he is getting a cold, and he cannot smell. You memorize the smell of the Heavy Stones.
You can find the four Heavy Stones in Chiro Caves B2. They are mainly around the northern part of the area, but if you are digging one up near a bat, make sure to run away quickly because the noise will wake the bat up, and it will attack you. You may have to let yourself get hit, because there is very little way to escape the bats once they are on you. Be sure to bring healing items. When you have all four Stones, go back to Chiro Caves B3.
You need to go up to every pillar and press 
to place a Heavy Stone. Once you have put each one on a pillar (and watch out for the Alligator) the door will open. Henry will thank you, and tell you that if you carry on from here you will get to the West Chilly Fields.
The Firewood
When you get to the West Chilly Fields, Petasi will tell you that it is freezing, and that you'll freeze over if you get too cold. Similarly to in the desert, you have a face in the top right corner and if it fills up with blue, you'll freeze. Except if you take a bath in the hot spring you can warm yourself up to almost burning and have more time before you freeze.
You will see a Weimaraner named Seigfried standing by a large block of ice blocking the way to the Snow Village. He will state the obvious and then ask you to find some Firewood to melt the ice block.
While sniffing around, you will come to a cave with a Polar Bear plodding about in front. Wait until it falls asleep and then stun it with your bark. While it is knocked out, search the cave with . Take it back to Seigfried.
He will thank you, and then you will see him make a fire and clear the path to the Snow Village. You can now go there.
Challenge with Gordon!
When you get to the Snow Village, go near the entrance to the East Chilly Field and you will find Gordon. If you talk to him, you will give him Bill’s message. But Gordon says that he only trusts dogs who are stronger than he is, and that he wants to challenge you to a Sled Race.
First you will have a tutorial, so you know what to do, and then you will need to race against Gordon (see here for how to play) and if you win you will get the Victory Gang Badge of Gordon. He then tells you that Jeremy wanted to see you. He says that he is in "this village" now but he is in fact still in his house in Pupsville.
The Magic Travel
Go and talk to Jeremy who is in his house, and he will remind you that you still need to help him make a Weather Rod. To do this, it must be dipped in Sea, River, Lake and Snow to gain the power of water. He tells you to use the sea and river at Green Meadows, Zoomy Lake for the lake, and West Chilly Fields for the snow. He then realized that he hasn't told you about Mana, and then teaches you the smell of it, as this is where you need to dip the Weather Rod. He then tells you to not just stand there... get going!
When you get to Green Meadows, go to the beach. Sniff around here and you will be lead slightly out to sea by the scent of the Mana. When you are in the right place, Jeremy will come and dip the rod in the sea. Then you need to walk along the eastern side of the river, and you will find the Mana here, and so Jeremy will come and dip the rod in the river.
Next you need to go to Zoomy Lake. You need to go onto the island that begins the path leading to Zoomy Village. Jeremy will come and dip the rod in the lake. Finally you need to go to the West Chilly Field. Sniff along the northern coast and you will find where the Mana is. Jeremy will come and place the rod in the snow, and now the Weather Rod will have gained the power of water.
Jeremy thanks you, and tells you that if you ever need help with rain down the street, just come and see him! He then tells you that Tao was looking for you.
The Secrecy of the Sniffing - First
If you go and see Tao in his Dojo in Gola Highlands, he says that you have been training well. Now, it is time for you to go and look for the First Book of the Sniff Master. He tells you that you can find it in the East Chilly Field.
When you get to the East Chilly Field, go towards the penguin on the ice. Petasi will then tell you that some of the ice is thin, so you should only step on the places which are thick. He then says that you could follow the penguin, as it will know where it is safe to walk. Go up to the penguin and bark or howl. It will then start running along the ice. Try and follow it without going off the path it takes. When it reaches the other penguin, climb onto the snow again. Go to an igloo on the south-east and sniff around it. You will find the First Book of the Sniff Master here. Go back to Tao.
He congratulates you and asks if you have checked on the Anc Tree recently, and says that you should go and see how it is doing.
Growing an Anc Tree 3
Go to Pupsville and to the centre of town where the anc tree is. You will see that it has grown. Petasi then says that you should go and see Tao.
In Gola Highlands, Tao will tell you that he has another task for you; to find the Second Book of the Sniff Master. But it seems you are not ready for that yet, so in the meantime you should go and see Will in Gigili Village.
Challenge with Will!
Go in front of the Inn at Gigili Village, and Will will appear. After you give him Bill's message, he will tell you that he only trusts dogs who are faster than him. Therefore, to get the Victory Gang Badge of Will, you must beat him in a flag race. Take him on and win, and you will get the Victory Gang Badge of Will.
He then tells you that there is a problem if you want to get the last victory gang badge; they live in Rune Village, which is beyond Dry Valley. You can get to there from the North Sandy Desert, but there is an enormous Sliding Sand blocking the entrance to Dry Valley, so you have to do something about it. If you go to the North Sandy Desert, there will be a dog there waiting for you who might be able to help...