>>what is a good light weight and well insulated coat to use. <<
As others have said... think "layers", rather than one "well insulated coat".
The air temp might be 0 degrees, but you will be hot, hot, hot, when hiking uphill. And the key to staying comfortable (and safe) in the winter is to stay DRY. You want to wear enough insulation to be warm, but not so much that you sweat. Having a number of layers, rather than a thickly insulated jacket, makes it possible to adjust to varying conditions; add a layer when you get cold, doff a layer when you get hot.
The sales folks at EMS should be able to explain and demonstrate the concept (of layering) using items from their inventory. It will be very similar to what the other responses to this thread have described:
- A non-cotton base layer
- One or more non-cotton fleece/insulation layers
- A gortex or similar windproof shell
To that **I** add a down or synthetic parka that can be worn OVER everything else - including the gortex shell.
Incidentally... the layering concept works for mittens or gloves, too. Rather than wear a single heavy glove, consider going with a thin liner/base layer, followed by a fleece, wool, Primaloft, etc. insulation layer followed by a wind/waterproof shell. That offers a lot of flexibility in terms of adapting to the outside temperature as well as the heat that you generate whilst hiking.
Again... the folks at EMS (or any other reputable outdoor store) should be able to demonstrate the concept and recommend products for each of the different layers.
You mentioned "sweatshirt" in your post. If it's made of polyester fleece it will probably work fine. But, as others have said, AVOID wearing anything cotton (including underwear) in the winter; once wet, cotton does NOT provide insulation and is very slow to dry. In contrast, synthetics and wool continue to provide insulation when wet.
The salesfolk will probably wax rhapsodic about "soft shells" - the latest rage in outdoor fashion. They're great pieces - sort of a cross between a fleece insulation layer and a windshell, but expensive. In some cases, VERY expensive. If cash is an issue, the softshells aren't necessary; you can get by perfectly well using "classic" fleece and a "hardshell" (aka gortex etc).