If they are really big puddles then yes. The horses will end up sliding around on the branches if they are large. As above try doing half or a narrow section that is good enough for cyclists. If you cover the trail the first horse to go over will end up kicking them all over the place anyway.
It is worth considering what kind of ground it is and how the horsists will move. They prefer to go faster up longer gentle rises where the ground is free of rocks. If it is rocky/very soft or downhill they are more likely to be walking so it would cause less issued.
Is there anyway you can get some drainage in (dig a channel or hole to the side) to encourage the water away?