Why WOULDN'T you wear your coat when it's cold???

So what's the deal with winter coats? Do your children wear their winter coats? We live in a climate where the winters are fairly mild. But it does get cold here. This week it has been in the upper 30s and 40s. But my 10 year old daughter wore either a sweatshirt or a poncho all week. She has a winter coat. She just won't wear it. Sometimes she even makes the mistake of complaining that she's cold. But she always has an excuse as to why she doesn't need/want her coat. Here's the usual scenario (assuming the coat makes it out of the closet) -- she carries it, at least until she can convince her dad to carry it for her.
And here's a photo with her actually WEARING the coat. I had to scour iPhoto to dig one up. And I should mention that we were in Chicago when this picture was taken.

I feel compelled to provide her with a coat. Wouldn't it make me a bad mom if she DIDN'T have a winter coat?? But after looking at a nearly new-looking coat hanging in the closet all winter, I feel ambivalent about forking out the cash to get a new coat to replace the one which she may have outgrown, but has certainly not worn out.

A coworker says she no longer requires her 12- and 13-year-old daughters to wear their coats to school. In fact, she confessed that her 13yo doesn't even HAVE a winter coat (gasp!) For me, I think I will keep buying my daughter a coat. This is partly in order to cross my t's and dot my parenting i's ("yes, your honor, of course I bought her a coat..."), but mostly because I want to continue to win the dispute we have when she tells me she's cold. I mean really, how would I counter that complaint if she didn't have a coat at home in the closet???