There is no harm. You can even say prayers with your shoes on. Who stops you? You know, in the mosque you can’t carry shoes because people have to bow down and put their foreheads in the place where the shoes would be placed if they were permitted in the mosque. So, to avoid fail to keep the mosque clean you take the shoes off. But while you are travelling and shooting for instance and the ground is hard or it’s thorny and it’s not possible for you to remain in concentration while praying if you take your shoes off.
There is absolutely no harm. Neither the Holy Quran nor the tradition of the Holy Prophet ever forbids you to say your prayers when you are outdoor with shoes on. Particularly while you are riding. The Prophet and his companions are known to have said their prayers while riding. And the questions were asked to him which way should we face while on a mount? And he said whichever way the mount is facing, that is the right way. So, they had their shoes on.
