serms can do this themselves. all of the PCT compounds we use are anti estrogenic in themselves, although they effect the HTPA system differently than an anti estrogen, the sides can be similar sometimes. anything that has an anti estrogenic effect can cause dry, red, scaley, itchy or blotchy skin. doesnt mean this is the case for everyone. anything that effects estrogen makes my face dry blotchy and sometimes red blotchy. this can also happen from the hormonal change from on cycle to PCT. as stated below we go from point where we make excess oils and when we stop the exogenous hormones it can cause a deficiency in those oils, the same thing happens when you use chap stick, i know its an odd comparison but when you put something in your body stops making it. so you may just need to wait till your body is back to normal. i use head and shoulders dry scalp as a body wash to combat this issue and it works great. keeps the dry and itchy at bay fairly well. i will also use a moisturizer soap if its really bad.

maybe its just the seasons changing rather than the cycle

I had a buddy that got super dry after his cycle. It eventually went away after a month or two. After talking about it and getting other people's opinions, we think it was just that his body was producing so much excess oil and such during his cycle, that it kind of shut down when he came off. Maybe similar to your test shutting down on and after cycle. Once things balanced out, he was fine. We didn't think it really had much to do with his PCT compounds (which were standard nolva/clomid). I don't know if this is what is happening to you, but I thought I would throw it out there.
Also, he never had any skin problems in the past. Have you ever been prone to this?