No I wouldn't bother rugging them , if you can hold out a week or so for the weather to improve even better as temps will rise at night soon enough and they will be fine.
Sorry but I really wouldnt clip and bath foals in this weather... I woild wait until its at least 20 degrees... nothing worse than giving them a chill!
I would say just keep an eye on it (this is what I plan to do anyway) and if its any worse by Wednesday call the vet and explain - they may advise you over the phone.
No don't worry I'm not going to rush in to anything, just going to keep an eye for a few days.
The vets are well used to me coming in to the practice with some pictures on my phone or a long winded explanation and asking what they think is wrong...so that wouldn't be out of the ordinary haha!
You will need to try and keep them clean and dry so if you do clip them yes you will need to rug them.
If you have access to electricity and an extention lead and they are quiet you could try using a hair dryer to dry them (you only need to wash the areas that are scabby not the whole body)
You could just monitor the situation the hair does normally grow back without intervention as oxygen can help kills bugs so once the skin is exposed and when the summer coat comes through that can help, though you have to be careful about mud causing an infection if the skin is broken and if it looks like there is any pus under the scabs or they are sore then you might need the vet as that can lead to needing antibiotics and then you would definately need to wash using the special shampoo.
It hasn't got any worse and there aren't any other parts of her body affected, and the other mini hasn't developed the same problem. So I'm inclined to think that it has been caused by the coopers burning her hair, however I will continue to monitor it. The patches on her face have turned out to be nothing,I think it was a combination of the hair lying unevenly and me being a bit paranoid as there is no sign of them now.
They are both moulting heavily now so hopefully it won't be too long until they have nice short coats which I think will do them both the world of good.