Well winter is really not too bad here Jif, particularly if you compare it with a Canadian one. You could always put on a pair of gauntlets, a fencing mask and other protective body armour and shave the poor cats.
That heat you're getting sounds a lot like Melbourne in late summer when the humidity sets in, really most unpleasant.
Current temp in Melbourne at 4AM is just under plus 12C, relative humidity 82% and we're expecting more rain over the next few days, and no, I don't want to swap.