If you're going to be active, you will benefit from layers. The most frugal approach IMHO is to thrift-shop a small selection of high-quality 100% wool sweaters: a lightweight, mid-weight, and heavy-weight sweater. If you're lucky enough to find a silk or silk/wool blend underlayer - pounce on it.
If you're into cold-weather comfort with extreme-frugality, make yourself a pair of wool "swants" from a thrifted sweater.
+1 best advice in this thread so far.
What kind of "outdoorsy stuff" will you be doing? Are you skiing in bounds or backcountry? Do you anticipate hiking or snowshoeing or any other physical activity (rather than just snowmobiling and downhill skiing)? If you are skinning/hiking/snowshoeing uphill a light base layer and outer wind blocking layer are your best bet. Dump heat as much as possible and try not to sweat. Anytime you stop throw on a down jacket to keep warm, do this before you actually feel cold. Much easier to stay warm than to try and warm up after feeling cold.
Personally I do not agree with the warm coat that is waterproof bit. I want my waterproof layer to be as thin and breathable as possible. Layering is much more versatile than a big warm coat, and if you need to shed snow or rain then a waterproof shell is better. Actually for dry snow conditions like you will likely experience in WY i would prefer a water resistant softshell jacket.
What kind of pants will you use?
Alos, maybe this is obvious, but it will be much colder as you increase elevation, and I would not count too much on the weather forecast in the mountains. Be sure to check avy conditions.