i would imagine that if it took place on public footpaths and not paths that have been negotiated the person would be liable irrespective whether they were on a challenge event or out on their own, negotiated rights of way then i would think the onus is on the landowner to make sure in negotiations he has regress, however it would look good for the organisers to point out any insurance cover whilst in negotiation

As a result of an enquiry regarding a no dogs policy on a challenge event organised by a Ramblers Group (and advertised on this site) I ran a search for dogs on this site and found the following

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Q. What is the position concerning dogs on walks?

A. The Policy does not extend to include any form of liability arising from the actions of a pet that a Member may take on a walk.
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Presumably walks includes challange events and I would not be surprised to discover that the insurance held by other organisations is on the same lines.

It is both the behaviour of the dog and the farm animals (farmers ?) encountered (regardless of how well the dog is controlled) that determines if there are problems for event organisers so I can well understand why some organisers have a no dogs policy.