You can simply sew on a belly band to whatever blanket is appropriate. You can use a slinky in the winter but you would probably need to put a blanket over it to keep the insulation factor since the slinky would flatten the hair. Depends on how cold you get.
It only takes about a 1/2 cup to 1 cup of flax. A good coat elsewhere is a good sign that things are ok. Probably just an allergy. The only way to pinpoint is to take away every factor, allow her to heal and add them back in slowly one at a time till you find the trigger. Just fyi, some horses are allergic to grass O.O dust wood oils..things found in every barn. You will have to be very diligent to find the trigger but it would be worth it.