My land is registered as an agricultural holding - 13 acres used just for cattle. The other 8 acres, is goats and horses. The problem does arise if you put in for planning permission (we have to for any building, wooden or otherwise here due to National Parks, areas of beauty etc. etc.)
Horses are domestic animals, and therefore when planning is requested for a stable etc. you have to change the use. If you are able to put up a field shelter without any planning, then that should be ok and you can keep your land in the classification it is. A mobile sheter can be moved, so should be ok.
But, out of interest, is there anything in the "rules" to say you can/cannot actually keep horses on land you are claiming the payment on? From what my neighbour told me, who has sheep etc., she said she did not persue the single payment scheme because of her horses being on some of the land? I have to say I have never tried to claim it, so don't know the answer to this.