I wash my vehicles whenever the temperature gets high enough to be able to do so during winter.
A film of dried salt on sound paintwork or the e-coating on the frame won't do much damage, but wherever it can get to metal through porosity of or damage to the coating will initiate corrosion - which then creeps under the paint.
What salt is used on roads ...
Sounds like your battery terminal connectors are stretched to the point that they are loose even when the bolt is fully tightened. Best fix would be to replace them with new connectors. Alternatively you could add a thin shim of metal between the post and the connector.
Since the metal lead (battery post) has a high thermal expansion coefficient, my guess ...
Lock your doors . . .
. . . and have a safe trip.
Weather is quite mild in Lubbock.
With the presumption that your vehicle is in good running condition, and has no charging system issues (like a bad alternator / battery, or an aftermarket alarm that constantly pulls 300mA,) you should have no issues electrically nor mechanically.
Silicone spray lubricant is often recommended by manufacturers for door seals, and it should work well in this scenario.
Not only will it help keep stuff from squeaking, etc, but it repels water, resists contamination from dirt, and has an effective temperature range of -100 to 500F
You can also use it in your lock tumblers to help them operate smoothly in ...
If the tires look OK, they are probably fine.
Issues to check for:
cracks in tread and sidewall
bubbles in tread and sidewall
cuts, embedded foreign objects
Storage conditions make a big difference. Storing tires in dark plastic bags away from sun light and ozone sources makes them last longer. Tires not mounted on a vehicle last longer.
Continental say 5/32" or 4mm- https://www.continental-tires.com/car/tire-knowledge/tire-care-maintenance/tread-depth
Some winter and all-season tyres come with an extra set of wear bars set at 5/32" or 4mm for when they're considered unsafe for snow use but they're probably still good for snow/ice-free roads right down to the normal wear bars. On snow/ice-...
It ultimately depends on how cold it is. As jwh20 said, the label will likely say.
That said, I couldn't find an exact temp marked on the packaging for the HT stuff. However, it's a little anecdotal, but DAP 100% silicone sealant can be applied as low as -35F and as high as 140F. Since these sealants are "partial drying" types, it would be best not to go ...
When a professional athlete warms up in the cold they don't walk slowly because it does not warm their muscles quickly enough and they don't sprint because they could damage something before their body has reached a good temperature...they do a gentle jog. It is not too different for your car; for the good of the engine, drive it straight after the oil light ...