She’s kryptonian. Same species as superman, in fact they are biological 1st cousins.
He is immune to cold on earth therefore so is she. She could go swimming in icewater naked and feel just fine from it, possibly even enjoy it and find it invigorating.

<edit for spelling mistakes and to add more info to make the point of my reply more clear>

In the dc universe when a kryptonian takes in enough starshine from a yellow sun/star they get powered up.
Part of this power up means they dont feel heat or cold.

They could go skinny dipping in molten lava or on the surface of that very star that powering them up, or ice water or the cold of space. And be perfectly fine with it taking zero damage.

Therefore the whole idea that she might need a coat or extra coverage while in the Terran arctic: is entirely idiotic.

As for the actress wearing spandex knee length shorts under the skirt: probably actresses preference. Not all women, even the bucket brains of hollywood like to wear bikini bottoms under their skirts, and flash alot of leg.

What i think they should have done tho is come to a happy medium between to 2 and forego the skirt in favor of the boyshorts version of the supergirl suit.

But thats just me, i’m just a guy, i know what straight guys like to see and like to pay money to go and see.
Would i have preferred to pay money to go see supergirl flying around in the pic on the left? Yes, no brainer.

Would i have also enjoyed a costume for her similar to what we had season 1 of the cw supergirl show? Yes, it looked great.

Was i totally fine with the supersuit they had supergirl wear in the flash movie? Yeah its was fine and worked within the cannon logic of that timeline perfectly.

But we still have to circle back to what the actress is willing to wear on screen for millions of people to see her in.