I train in an unheated garage during winter, where temperatures often hit freezing. My tip is to dress like your going hill walking. Avoid cotton sportswear. Get a decent base layer (one that's long enough to cover the lower back while squatting, etc), that wicks moisture away from the body, then a fleece or two, which performs the same function, as well as a hat.
Tracksuit bottoms are usually sufficient for the lower half
I find this sufficient to have a good workout undistracted by the chills. However, it also depends on the workout. During a recent phase I was resting three minutes between low-rep sets, and this meant popping on another fleece jacket between sets and doing some mobility work.
For some reason I train well in such conditions. During summer months (well, a few days in Scotland!) the garage turns into the Sahara. This means training in my underpants only. What a sight!!!