But is a tow path a public highway?
If it is not, then using a vehicle that would be illegal if used on the public highway, would arguably not be illegal when used on something that is not a public highway. You used to need a special permit to use a bike on the tow path, indicating that a tow path was not a public highway, but I don't know if subsequent legislation has changed the towpath's legal status. Perhaps it would be covered by by-laws or conditions of use, which could mean it would be a civil law matter rather than a criminal law one.
The last two times we hired at easter, it snowed. The first time it settled and was heavy enough to build a snowman figurehead.