I have an F-Type V6S (RWD) and it is my daily driver, but I can't help you with personal advice on snowy conditions as I have never seen snow on the road in my life!
But lots of info on driving the F-Type in cold and snowy conditions over on the US forum here: https://www.jaguarforums.com/forum/f-type-x152-72/
From what I can gather from that forum the F-Type V6S AWD is perfectly OK to drive in cold and snowy conditions providing you fit proper winter tyres and use ice/snow mode.