It's a yes without a doubt. Warmers and a genny cost a lot less than repairing a bike and ultimately repairing you.
if you think for one minute that those without will be taking it easy into the first corner you have never seen a club race have you ? The first corner is the most exciting bit, but also the most dangerous and you will have no time to think oh hang on my tyres aren't warm. Even if you did you may have to take avoiding action which is very likely and your colder tyres won't handle it. On a cold day the situation is even worse.
Don't compromise yours and others safety cos you can't afford to go racing properly. If someone took me out cos they were on cold tyres I would be very upset with them, there is enough risk without creating more.
I would like to see a control tyre in this series, altho warmers should be personal choice taking into account what's been said