Your first Winter
What you focus on doing during winter depends very much on how far you’ve come in the seasons leading up to it. Normally it is a period where you are free of the daily watering pressures, meaning you can do a lot more mining, fishing, and woodcutting. (And making friends with villagers, including courting a potential spouse.) It is a good time to bring tools to the Blacksmith for upgrading. Unfortunately - your income will drop, maybe a lot, maybe a little, depending on how well you have prepared.
If you’ve got stored produce, make sure you have enough Kegs, Preserving Jars, etc, to keep up with it. A single Pickled Pumpkin sells for 690gp, more than twice what a basic pumpkin would sell for. Kegs triple the value of fruits by fermenting them into Wine - although it takes 7 days.
You shouldn’t have to water crops outdoors in winter … except that once you complete the Winter Forage bundle, you’ll get Winter Seeds that will grow into these crops. These want to be planted outside and naturally *they* want watering. Winter seeds can also be obtained in lower numbers by crafting from a few foraged items, or by using a Seedmaker on Winter Roots.
As you are not sinking large chunks of time and energy into watering crops, winter is an excellent opportunity to collect resources from off your farm. Upgrade your axe and take it into the forests to cut down lots of trees; a thousand wood is not too much. Clearing trees on the farm is also a good idea - don't clear everything, especially not if you have tappers attached, but you'll probably want to plant larger areas in Spring.
Get some fishing done - there are a few fish that are best caught in Winter, and you'll need them for the Community Centre.
Pursue metals in the mines - if you're in the normal mines, you may be able to work your way deeper nearly every day; if you've reached the bottom and got the skull key, then you need the money to complete the Vault bundles and get the bus to the Desert going again. That will let you access the Skull Cavern, which is dangerous and demanding but an excellent source of the three regular metals and almost the only source of Iridium. Small amounts of iridium, combined with a few batteries if you were able to get lightning rods before the end of summer, will enable you to make Iridium Sprinklers, which go very nicely in the greenhouse. Larger amounts of iridium will let you upgrade your watering can, which will position you to water quite large areas of crops in Spring.
If you have the Greenhouse, that will keep growing produce but of course it still wants watering. (Even if it rains.) You can do a lot to keep your income up by growing crops in here. Make a high priority of organising sprinklers for the crops you plant in there; you may not have any iridium yet but 'Quality Sprinklers' can be made from lesser materials. Plant Fruit Trees around the outer perimeter of the greenhouse - they do not need to be planted in the centre soil, they can be planted right against the wall, or against greenhouse features, but you need two blank squares between any two trees, and you may need to keep the inner perimeter clear until the trees are fruiting (obstacles too close to trees prevent them growing.) You can fit 18 trees around the Greenhouse - just start with one next to the entrance and work around from there. Once they have grown they will produce fruit every day for an excellent ongoing return - normally a fruit tree pays back its investment in one season and you make profits in the following year, but greenhouse trees never stop fruiting.
To get the most out of the Greenhouse, try to get some strawberries and coffee beans growing in there. Both plants make excellent cash crops - but it's not the cash from the Greenhouse produce that we're looking for here. It's the seeds; neither seeds are readily available. Kill Dust Sprites (iron levels in the mines) until one of them drops a Coffee Bean, then plant that in your Greenhouse, and when it ripens (a subtle change) replant the seeds; 5-6 coffee bean plants in the greenhouse for most of winter will let you collect on the order of 100 beans to plant at the beginning of spring. Coffee plants generate 4 beans every 2 days and sell for 15gp each, so the plant yields 30gp per watering for most of spring and summer!
Strawberry seeds are only sold at the Egg festival halfway through Spring, and they manage to be profitable even if planted then - planting them at the beginning of spring means you should get 5 harvests instead of 2. So if you've saved even 1 strawberry from your first Spring, you can put it through a Seed Maker and plant the results in your greenhouse; when it fruits, put those through your seedmaker and plant again; if you managed the greenhouse at the beginning of winter then you could readily have 10 strawberries fruiting by the end of winter, and 30-100 seeds depending how many seeds you got from that first strawberry.
By the end of Winter, plant some Summer fruit trees outside. Make sure you have still have cash on hand - you’re going to be buying seeds again!