Its 4H - not a kindergarten class. Yes, there will be young kids and livestock. There will also be adults who have experience around livestock presumably (after all, they are involved in 4H and presumably were in it when younger).
As long as there is a reasonable adult to child ratio (say 5-6 children per adult if under age 8-12) and split into smaller groups if more than 20 potentially - cannot see there being issues.
Assuming you have insurance, your fine there. After all - the club would be primary (as they organized the trip). Each case is very individual - so cant answer much to that end - but as a high level overview - you would be covered by most any homeowner/farm policy for guest.