Depending on what I'm hunting I always check the moon phase. I generally don't book hunts during full moon. Maybe that's just me, for sure many hunters will say it's the best time to hunt and they always kill their biggest bull/bucks during full moon.
If the moon is full during the day it can be awesome. If it's up all night it can make daytime movements slow down, but if weather comes in and covers the moon at night, I've found the weather can be a larger factor to consider.
The moon phase will never be something that causes me to choose one season over another.
I got my first elk 4th season after the super moon, was like walking in during daylight. Biggest herd I have seen about an hour after sunrise. So it certainly is possible.
Full moon and hot, dry weather can be extremely tough. Elk may only be active super early and late in the day. If you hunt during mid day you may spook them out of their bedding areas. If you are hunting an OTC unit with lots of orange it may make a tough hunt even tougher. You never know what will happen but can be some super long days twiddling thumbs if the weather is warm and dry. With that said, if you luck out with cold, snowy weather it may not matter as much.....especially in a limited unit with fewer hunters.
If the full moon makes them feed art night and sleep all day, which isn't too much different than what they normally do, I'll just go kill them in the timber.
Is been slightly tougher under a really full moon during the day, but I've still been successful.
2nd season in CO is 9 days long and almost always has weather at some point.