I have been installing sub panels outside for close to 20 years with no problems.
If you are concerned about the breakers and heat, put some form of shade over the box. This can be accomplished in any number of ways: put the box under a patio cover, plant a bush, hang a plant, paint it a light color (match the house?) tuck it just around a corner, put it in a box with a hinged lid/door etc.
I like having the GFI breakers in the sub panel for several reasons, not the least of which is simple economics: HotSpring ships the GFI breakers that we need to use in a GE sub panel, included in the price of the spa. Also, they are covered by the tub warranty.
But other reasons I like having them out near the tub are:
eliminates the need for another shut-off device (main reason here is the extra junctions that puts into the various circuits - esp. ground)
the breakers get tested when the user drains the tub
you can shut off the heat only if you want to cool the tub
easy troubleshooting - on the phone I can ask which breaker and that tells me a lot.
our boxes have room for another breaker (or two) for add'l circuits.
They come in a nice, nuetral grey color that goes with everything