What is the regulation(s) for being put on orders and/or deployment if ta-50 or hot/cold weather gear has not been issued?

There are plenty of regulations about this.
But that won't stop the order, that will just ensure that they won't leave the unit to go work somewhere outside until they have been issued cold weather gear.
That might be an immediate hand receipt with stock available at the unit, or a trip to your state's CIF.

TA-50 will be issued at the MOB Site. When my Guard unit arrived at Camp Shelby we turned in the state issued ACU gear and were issued complete sets of Multicam gear and uniforms for deployment. If you are talking about local call ups for cold weather response here in the states I doubt you will be called on to survive all night outdoors. Just make sure the heater in the HUMVEE is working!

Probably have to cross load with soldiers that have the gear.
As a grunt in my first unit it I wasn't issued wet weather gear unit a few months before I transferred to another state (in that unit for 3 years). Plenty of times I was in single digit temps in deep snow and the unit just shrugged their shoulders. It sucks and I'm not saying that makes it right but that's the military for you. Your comfort is not their top priority