There are 4 sections. The A is the Welsh Mountain Pony; The B is the Welsh Pony; The C is the Welsh Pony of Cob Type; The D is the Welsh Cob. Some refer to them all as Welsh, some do that but add the letter.
I LOVE feathers and would NOT want to cut them off, even on your beautiful Welsh Cob. But, if there were a medical reason to do so I would have to face it and do so... crying if it were my Fell pony and his gorgeous feathers! But really, it's totally up to you, and if you want to take hers off, no harm to her at all! :)
BTW I just bought a Welsh Mountain Pony who is red roan and I thought of your girl as soon a I saw her :)