This will seem like a real Idiot's Question, but here goes…

I have a Ridgeback Genesis Day One road bike, circa 2004. Is this in any way related to the Day One by Genesis, other than having a very similar name?

Reason I'm asking is that I'm toying with dabbling in a bit of cyclo-cross next winter, but I don't know how into it I'll get. I'd rather not bring ANOTHER new bike into the house on a whim, so my idea is to change the spec on my existing bike, just to get a taster of the sport – I can always bite the bullet later on if I get hooked. So (a) will my bike fall apart as soon as I point the front wheel off the tarmac, and (b) what should I be looking at changing?

Thanks very much!

Is it your only bike or do you have a mountainbike as well?

The main problem I can see is clearance or lack of it for cross tyres. I have seen people race old road bikes with mudguard clearance, but that bike seems to be pretty tight. And tyres nowadays seem to start at 32mm, old tyres were narrower.
You bike otherwise would be ok, it certainly wouldn't break.
But clearance will be the problem, though last season I don't think our region had a single muddy race.

like oldgit says, clearance could be the issue. try and race as early in the season as possible, the start of last season really was very dry.

have you got any pics/links of the bike?

Assuming you have a mountain bike then I would try racing on that to see of you like it. A lot of people do but you'll have to check with the race organisers if MTBs are allowed or not.

What oldgit says – cross bikes run canti brakes in order to get the clearance for cross tyres. If you've got regular calipers, then you'll be unlikely to have the room.

Put some 26" cross tyres on your MTB (like the Schwalbe ones I run when I do the odd bit of cross) and see what it's like. Plenty of cross races will permit you to use your MTB, and it's a great intro to cross racing.

This perplexes me:

will my bike fall apart as soon as I point the front wheel off the tarmac

There seems to be a real assumption that road bikes are made of glass and will shatter into a thousand shards if not ridden on super smooth tarmac. They're pretty robust, as exemplified by this sort of thing: