Shortly said: “Does head hair grow faster in cold weather?”
Just the opposite. http://www.afraidtoask.com/hair/hairlifecycle.html
An inch per month!? Most people get about 1/2".
Personally my hair grows 6-8" per year. It’s fairly even growth (about 1/2" per month) but sometimes I’ve seen a ‘spurt’ where it grows an inch or two in a month or less, and when that happens it’s been in late summer. Yes, I’ve been measuring and charting my hair growth for about 5 years now - don’t ask.