I want to start off by saying that I'm brand new to the game, as I started playing only by a week. Keeping that in mind, I am not 100% sure if the testing I did is completely accurate.
Anyway, according to the wiki the Horseshoes (http://www.wurmpedia.com/index.php/Horse_shoe) do not increase the moving speed until the QL of every individual horseshoe is 50 or above, or until the summed QL of the wore horseshoes reaches 70.
Total Shoe Quality
Speed of the Horse
1 - 60 QL
70 - 130 QL
I did some short tests and I noticed that my moving speed while commanding a cart with hitched horses changed whenever I removed or put horseshoes from my horses.
As you can see in the top left corner my speed is between 12,99 and 13,00 km/h when both my horses are wearing horseshoes.
It drops significantly to 12,23 km/h when removing the 46 QL horseshoes from one of my horses.
It remains at 12,23 km/h even when decreasing the summed up quality of the remaining horseshoes below 70 by removing one of the horseshoes.
With no horseshoes on at all, my speed decreases to 11,48 km/h.
Sorry in advance if this topic has already been brought up by somebody else or if my testing was not made correctly.