I am a wimp when it comes to the cold too, but I try to stay outside until my races for the winter are done. But once it's below freezing (or feels like freezing) I'm done. It takes me all day to warm up, even with 2 pairs of pants, although I feel fine when I'm running. Once I stop I notice the cold, and my arms and legs literally stay cold all day.
Find a good spring half! It's a great experience. Even if you don't enjoy it, for whatever reason, you won't regret trying it.