I use a hand towel. The corner by the tag is for nose. The rest is for forehead.
Snot rockets…straight onto the floor. I’m in the garage, concrete floor with mats under my rollers/trainer, I just make sure to clean them every couple weeks.
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I always keep Kleenex but find I need them mostly as it gets cooler. After a quick blow I throw them over my shoulder to try a no-look into the trash can. My kids love it and laugh when I miss.
I use a hand towel.
I’m in an unfinished area… so I admittedly do this on occasion as well, then use my sweat towel to wipe the area down after I’m done. I don’t want to wipe my face down with snot mid-ride.
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I grab a kleenex, and then sit up on the saddle which gets my face out of the fan wind stream. This makes it really easy to execute the blow your nose on the trainer maneuver 
You likely have runner’s biker’s skiers nose. Try arrive to nasal. Decongestant pills used infrequently help. Nasal decongestant drops are not advised because they can cause rebound runny nose when you stop using them.
Atrovent nasal spray