Hard to crank on a cold start but once it cranks it starts fine from there on. Why is it so hard to crank on a cold start?

what is it doing? you said starting. like is it not cranking over? because you mentioned the charging system.
or is it not firing up when it cranks over? because you also mentioned starting system.

i would return the mule to the dealer where you bought it,and let the warranty pay for the battery and testing,etc.

try cranking it with your hand completely blocking the carb intake for a few cranks. that sometimes helps blow out the passages.

Hey Dave, will the starter turn the engine over at all?? Just because the battery is showing 12V+ does not mean it has any amperage (amperage is what starts your engine - NOT voltage)
Your battery may be getting old... take it to O'Reilly's, AutoZone, or your local battery shop and have the CCA (Cold Cranking Amps) checked, then you will know the real condition of your battery.
Once you do this, if it still won't crank, reply back to me on here.

check your crank seals

My lawn tractor with a Kawasaki engine had the same problem. I found that the linkage for the gas throttle had a lot of dirt on it and would not let the throttle close completely. So when I shut off the warm engine, gas leaked into the cylinder. It would take a lot of cranking to start. When it did start, the exhaust put out black smoke.

The number 1 problem with ATVs is the carburetor. This could be a mixture problem... too rich will cause backfiring and difficulty starting as the carb needs more air. Try leaning it down a 1/8 turn. The choke is always intended to be used when starting; if you don't need to use the choke, the card is definitely running too rich. If you can't adjust to make it behave properly, then rebuild the carb, It's not difficult.. get a new throttle spring and float too. Ensure you place the keeper clip on the correct groove of the needle valve... where the throttle cable connects. Replace all the jets and gaskets... don;t get them mixed up. One larger jet is the primary jet and the smaller one, is the secondary. Get new screws, if the screws are a bit dog eared. Write down your previous mixture settings and start from there to adjust the mixture for starting and assure a slightly skipped idle. (Don't worry as you add throttle it will run smoothly.)

Try replacing the solenoid, which is attached to the starter.
To test, run it until hot,let it sit for 5 minutes, try to start. Then, go and tap the solenoid with a hammer ,and try to start again. I bet you it will crank over.

Try checking valve clearance. I had a Honda that did same thing, Set the valves and would start right up when cold.

sounds like lack of compression