In the cold hall, if you HAVE to sit down for more than a few minutes, understand that the majority of body heat loss leaves from head, armpits, and any open exposed clothes... (Think your neck and man-zone.)
Covering those areas when sitting makes a lot of sense. You do not need a ski parka, face mask like balaclava, and snowman scarf... but basic equipment helps.
Wear a watch cap, wool or microfiber. Wear a neck gator. Buy one or make one. Zip up the jacket over the neck gator to stop loss of heat from chest. Bring a small blanket to score table. unfold 1/3 of it and set it down where you sit... this will help with insulation and big heat loss. Fold the other over and tuck it in if there is enough. Wear micro fiber fleece gloves if needed. if the arms are a concern, use sleeves or long sleeve shirt under TT uniform.
Once you get up and move around, you will not be cold, you will actually sweat.
That brings up another problem... now you are wet and it is near zero... once that happens and you sit down, you got a huge problem in the making. That means major heat loss and you are soon not just back where you started, but worse. You will be hard press to reproduce heat during and immediately after major heat loss.
You may git a little frigid taking off your shirt and drying off quickly, but you move around and you will be fine. If underwear gets wet, that is a huge problem, bring extra underwear and change if wet. If opponent doesn't like that you need to go to bathroom, tell them you got a national emergency mudslide to attend to and ask them if they want that stuff on the court or flushed safely down a toilet.
At a minimum, have a watch cap, a 1/2 blanket, and neck gator in your bag, they do not take up much room and will help you with 90% of the problem.
If one does what is practical and gets some reps in cold halls, then later, one has an advantage playing in a cold hall.
I still stand by the bat needing to be warm and still stand by the idea that is pretty easy to get and stay warm. (if one is basically prepared) If someone is not prepared, then they pretty much asked for what they got.
If someone want to go on a huge hiking trip in dead winter in a remote area with no water, no survival gear, no cold weather equipment or communication... then what do you think is gunna happen? I read about stuff like this every month.
Basic preparedness and skill and planning go a long way.