Not only are YOU uncomfortable, if you are turning "plastics", they become more brittle and more likely to "blow up". "Torpedo" heaters have dropped in price and they are very powerful!
Not turning plastic? Wood will turn fine in the cold--finish---not so much!!! Read the label and work within the recommended temp range. Otherwise, you may see peeling and other unfavorable reactions.
If you can't warm your shop, delay making pens!!!
FWIW,
Ed