A few years ago at HITS Tucson I had my young horse shorten his stride in muddy conditions. It had poured rain for a few days straight, and I think he was a little unsure of his footing in the slippery/muddy conditions. I just added down the lines that day, as I didn't want him to get worried. I would imagine this could happen with any horse.
I've never seen a difference on grass vs. sand rings, but I suppose if it were slippery it could happen
I am home on call and tired of the Olympics-until the Hockey final at 3 anyway. So I'll bite...and have shown on about everything.
IMO it does not change much in actual stride length, matter of a couple of inches, but changes the way the horse moves to cover it, how hard they have to work.
On hard ground...which can be grass, something compacted pretty hard or just plain old hard and smooth ground? Most move pretty easy-tho some will get a little footsore and start showing it in not wanting to reach forward in front or track up so far behind.
In softer ground like sand over a base, shallow mud or mud over an all weather base in good condition? Not alot of difference at all. Most are fine and won't slip or "climb".
But with too soft and deep footing, deep mud or mud with no underlying base? they have to use more up and down and sort of "climb" to get the feet out of the mire and that will mean a shorter stride. Water splashing and hitting their belly usually makes more up and down too-or that you scratch. Deep stuff they have to climb out of with every stride kills suspensories.
Uphill they do have to work harder and might shorten a little. Downhill lengthens them but puts them on their forehand and it can be a wash.
The course effects stride length more then the topography...assuming a 12' line against what the horse wants it's kick up the first line at 11'6", second should be perfect at 12'. Ease the third at 12'6" and cool your jets on the last line at 13'.
Away from the in gate goes to 11'6", towards the in gate can get to 13'. And Lord help you if that last line is heading right to the in gate, downhill over firm ground.
When opportunity knocks it's wearing overalls and looks like work.