Adding to what was already mentioned above by dogsnadgers...
The chain width is the same. It's 3/32". These chains were the standard size that all bikes used from 4 speeds through to 8-speeds inclusive. Chains got narrower when 9-speed was introduced.
In terms of fitting a 7-speed freewheel, you need to ensure that the thread is the same on the hub as the freewheel. There is English, Italian and French threading. Most hubs and freewheels are English threaded, but I have a set of late C-Record hubs from 1990 which have French thread, so it's worth checking just to be safe.
If the threads are the same, then the only issue is chain clearance as already stated. Put it on, and have a go. If the chain rubs against the stays, you can put some spacers behind the axle's locknuts to widen the clearance to stop the chain from fouling the stays. You may need to pull the dropouts apart to get the wheel in, but it's not really an inconvenience. The only other issue you might face is whether the axle is long enough to sit in the frame once the spacers are on. It's worth checking that enough axle is sitting in the dropouts to hold the wheel in place when riding.
Anyway, give it a go, and see.
Last thing. Put lots of grease (or better yet, anti-seize), on the hub threads before you put the freewheel on. Without grease, the freewheel will be a right bugger to get off after a few years of riding.