Depending on your tolerance level and few other things, how cold it really is, rain or not, wind ..etc.
It doesn't matter what the temperature is (low wise), even if you are well dressed it will still get to you eventually, it is just the matter of time. If you are doing a full day ride I would suggest getting heated grips, long johns, wind breaker pants an jacket, and most importantly know your limit before you start drifting in the thought of "I should have stayed home". I had few of those moments and it wasn't pleasant.
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