On many diesel applications that use glow plugs and grid heaters, the Powertrain computer commands the alternator off during the initial warm up while the glow plugs and or grid heaters cycle on. Once the glow plugs and grid heaters cycle off and the PCM turns the alternator back on, this is done to take the severe load off the alternator and let the batteries do the work during this initial start up cold. Maybe your coach does not use this strategy and the belt is indeed trying to slip when cold as stated by others.
Another thing to try is unplugging the alternator or pull the alternator fuse and start the coach under the same conditions and see if it still acts up …that will tell you if the alternator load is making the belt slip... or not.... and is or is not your issue.
That being said it shouldn’t slip at all in any normal condition. cold or not.
If the noise goes away with the alternator unplugged or the fuse pulled, you now have a direction to head for a resolution.
It could be as simple as a wrong belt, bad belt or dirty or rusty, pulleys.
Could be a simple belt adjustment and have to be tightened ( if applicable)
Could be belt adjustment even if it has an automatic spring loaded tensioner and is the wrong length belt and that the auto tensioner can not do it a proper job.
You want to make sure the auto tensioner is not at the end of its travel ( either way) once the proper belt is installed.
This auto belt tensioner Pic if for reference only