With cycling it’s complicated because different canals and even different sections of the same canal have different rules. Most towpaths where cycling is allowed you are supposed to obtain a free permit.

There is a website that has the details of where you can cycle, for example the Oxford canal,
http://www.waterscape.com/Oxford_Canal/cycling/wid59;mine436144;maxe454702;minn206379;maxn284658
Unfortunately I’ve never seen that info signed on a towpath so I’m not sure how to get it into OSM.

Horses I believe are not allowed at all. At least many of the paths I’ve seen are in no fit state to support horses, many are bad enough on foot.

I’ve just been tagging them as highway=footway.
Also I’ve been taking note of bridge numbers and tagging the bridges with a bridge_number key. Bridge numbers are a quick and easy method to work out where you are on a canal so should really be recorded somehow.