How many wide mouth Nalgene canteens would you carry for a 3 day winter trip
Sounds like an arithmetic problem to me. (Daily water needs divided by how many times per day you expect to be able to make water).
Regarding size, I lean towards 1 liter containers. I bring two one liters plus the 1/2 liter mentioned below and expect to make water morning and evening (except the first and last morning usually)
maybe a 1L bottle for keeping inside your jacket against your chest.
I use a 1/2 liter platy in a fleece pouch hung from my neck. I find a liter too heavy for that use but YMMV on that count. The half liter comes to bed with me, nice for wetting a dry mouth and also nice to have warm water for the first drink of the morning. I also find that I can more often make it through the night without a trip to the pee-tree if I sip during the night rather than cameling up before bed.