Being in Switzerland we are supposed to have winter tyres on at the moment and have chains in waiting in the boot.
Luckily when I bought the car it already had winter tyres on the alloys. 195/60/15 I think. Someone off ebay.ch was then selling set of wheels complete with the same alloys as mine and Firestone summer(/normal) tyres (which he said hadn't done more than 10k miles)--he had upgraded to a boy racer set. Anyway I paid CHF 360 / £150. Two options: buy some rims and get some tyres on them if you want the possibility (like I do) to fit them yourself every winter or get the tyres changed at kwikfit or whatever and have them re-changed in spring next year.
The chains you can buy over here in the equiv. of Halfords. So try Halfords there. As a last resort I'm sure you can get them in the German motorway services on your way over (for a price maybe). The Germans are pretty keen on safety. You may find the Czechs and Slovaks don't even bother... especially on older cars.
Just make sure you get the right size. A set will contain a pair for affixing to your driving wheels (in our case, only one set for the front is needed). Remember you can't drive over 30 MPH with them on and only put them on when you can feel your car slipping--You can drive in snow quite comfortably with the winter tyres. Make sure you have some gloves too, because it can be f'ing cold when putting them on (especially for the first time) when it's snowing (maybe it's wise to do a practice run before getting into a situation). I found that after putting them on, they need re-tightening after the first quarter of a mile.
They're are other things that you are supposed to have in one or more European countries which I forget now... they usually include things like first aid kits, reflective vests, etc. but whatever. I would advise a GB sticker, light deflectors, warning triangle, your V5 logbook (as proof of car ownership), insurance doc (green card at best) and driving licence. There's no "producer" over here and they'll be p****d off if you don't have these documents. When I've been stopped they always ask for driving licence and my 'fahrzeug ausweis' (vehicle identification--V5 log book in your case).
One more thing before I forget: If you fancy going for a romantic drive around the mountains on the Slovakian/Polish border, then remember it's going to be cold. Make sure your coolant (and windscreen wash) can cope with the minus temps). Oh and one other thing.. European breakdown cover: Don't forget it and check that it's valid for the countries you're going to and through!