Here is a short description about how shoes affect the tolting horse.
Tölt III.  
Shoes and Boots. 
By Arnthrudur Heimisd
How the horse is shod is of great importance for the tölting horse. 
Even a weight of 100 grams has often a lot to say about how the front foot moves, but weights make little difference on the hind feet except it is more than ca. 400 grams, so they are rarely used (except as heavy shoes). 
Weights, whether you are talking about boots or shoes, cause the foot of the horse to take longer  steps and bigger steps than a foot without weights. 
Remember that heavy shoes and boots cause extra strain on tendons and boots can easily rub the skin on the horse's foot until it's very sore.  If using boots, check the feet before and after every ride, to be sure that the tendons aren't swollen and the skin isn't sore. 
But it is often helpful to use heavier shoes for maybe a two months period, to help the rider to clean pacy tölt, instead of endless work with the reins, seat etc. , and can be easier on the horse.  Using heavy shoes or boots for long periods of time, or every time you ride the horse, does though not teach the horse to gait correctly, it gets used to carrying the extra weight and the effects of the boots are lost again. 
Using boots is also common in competition, to get the finishing touch on the horse, with more action and cleaner tölt (if the horse tends to be pacy).  But then it is best just to use the boots a few times or not at all between competition, so as not to get the horse sore or loose the effect of the boots. 
If the hoof is allowed to be long, it helps to clean pacy tolt and give more action, but it also raises the risk of cracking the hoofs and breaking the heels. 
If a trotty horse is shod, it is best to use light shoes on the front hooves, even no shoes if you can.  Keep the front hooves short.  Using heavy shoes on the hind feet for maybe two months can help, but often makes little difference. 
If a pacy horse is shod, use weights or heavy shoes on the front hooves. 
Remember, all these corrections with weights, shoes and boots are meant to be used for a short period only, 2 months or less. And also, that traditionally, weights on icelandic horses do not exceed 10 mm thick shoes and 250 gram heavy boots.