Looks like baby checking, just starting, it'll get better. I'd be tempted to take it outside when it's 0º and then bring it back in the house, does wonder if that's what you like ;[]
As far as cleaning, a damp cotton (old t shirt) cloth, or your breath works as good as anything,
If I have serious cleaning issues to deal with, I use Meguiars Cleaner/Wax, no silicones in their products.
Wax on wax off.
Never EVER EVER squirt any product - or apply wax - on a guitar! Spray or apply a little on your cloth and rub away.