When we moved our pair home 2 years ago we invested in some mobile shelters from Redmire. However, we did check with our local planning department first, and took a note of the date and name of the council officer spoken to (for future reference!). They said they had no problem with them. Its a good job we checked tho, as we've had oodles of trouble with our neighbours - who have repeatedly tried to get them dismantled / moved!!!!!! Unfortunately for them tho, the council had already agreed that they were planning legal.
YES, they do move in a strong wind, BUT, we had a large wooden post knocked in and a chain wrapped around to prevent this later on. This makes them technically still mobile, but a lot safer and a lot more wind proof. Do be careful and apply caution, because although neighbours might say to your face they have no objections they may go behind your back (which is what happened to us with the other neighbours). (Sounds like we are surrounded by them doesn't it?! lol).
On the whole, I've been impressed with them, as you would not know that they are mobile and they look just like the real thing! We put down thick rubber mats - again supplied by Redmire, tho the odd thing is, it took me a while to get used to the fact that they weren't absolutely level - it felt like being in the fun house at Blackpool for a time, with the sloping floor! the horses didn't mind tho!!!!! (I'm not talking a steep incline here, just a slight one).
If I had to do it all again, I would definitely sneak some hardcore down in front of them, as they ended up in a terrible churned up mess. I did put down field mats (supplied by Redmire) but in the end they disappeared practically under the mess of mud!!! Of course in an ideal world I'd have no nosey neighbours and would have put in planning permission for a concrete base and got it! (without objections I mean!).
I know have deluxe "proper" stables - with a concrete base - but thats quite another story of how I managed to get planning permission..............
Hope this helps you choose anyway!