I've never smoked cheese but I have cold smoked in my MES with an
AMNPS.
Word of advice, stale smoke will impart a strong not so great taste to the cheese.
Stale smoke was something I encountered when cold smoking Salmon Lox. My salmon turned out fine but had to "mellow" a day or 2 in the fridge to shake off some of the stale smoke flavor.
Stale smoke happens because when you cold smoke there may not be a draft to suck the air and smoke up and out of the smoker like there is when you hot smoke. The draft is caused when the inside of the smoker is hotter than the outside of the smoker.
In higher temp areas like Arizona (or TX for me) you likely don't have the luxury of a 30-40F outdoor ambient temp which would allow you to put your smoker at like 50-55F to cause a draft without melting or cooking whatever you are cold smoking. This means you likely don't have a draft and therefore you will likely encounter stale smoke.
I made a little contraption which seemed to solve my stale smoke issue. It is cardboard rolled into a tube shape and a 12V computer blower fan that is angled up the tube to blow air upwards through the tube. I put this contraption over my MES vent and the fan creates suction up the tube which pulls air and smoke through the smoker helping it circulate and avoid becoming stale. I think some guys have just put a fan on top of their MES that blows OVER the top vent which does something similar but I can't confirm this. Here is my little contraption to give you an idea :)
Anyhow, if you read up on cheese smoking you will notice a lot of people saying the smoke flavor on the cheese has to "mellow" out for a few days. I believe this is due to stale smoke and my experience with cold smoking but that is just my hunch since again I haven't done cheese but I have battled stale smoke while cold smoking.
I hope this info helps and best of luck! :)