Tell them it's normal...maybe she feels safe in them. They could be her safety net. Another idea is let her wear them but tell her since it's cold she has to wear pants/sweats over them when she is outside. (this will help with the warmth)...it's all about compromise...
I agree with some of the other posters...this is not a big battle...go buy several pairs and let her wear them. Could be worse...could have my daugther who won't wear a coat because the seams hurt her...won't wear a hat because it's too tight on her head, must have tagless underwear and the best of all only wears specific socks and the socks must be in the CORRECT position or it's a total FREAK OUT.
Tights everyday as long as they're clean...I would take it in a second if my daughter would even remotely go near tights. Again it's all about compromise...strong willed children need to feel in charge...and as parents sometimes we have to let them feel in charge, even if it's buying several pair so you don't have to wash them everyday.