Winter tyres are great but not everyone can afford them, although I think some places let you 'rent' them and they'll store your normal tyres till after the winter. Our car is a manual but one of the work vans I drive is an automatic (it has no winter mode). It is harder in the auto to feel the vehicle as its about to slip like you can in the manual and take action, all I can say is to take it easy and be gentle with it, if you feel it is going to slide, ease off, correct and try again gently, try to keep your revs down as much as poss. If you come to a complete stop on a hill though it can be difficult to get going again, but better that than sliding into oncoming traffic!.
Get your existing tyre treads checked, any decent tyre place will do this for free, get a second opinion if you are told they are too worn, just incase someone is taking the P. Is your car rear wheel drive? They are notorious for being bad in the snow!
My tuppance anyway hope this is of some help.
EDIT- Crap spelling.