We're installing a new soaking tub in our bathroom renovation. The floor is completely gutted so we can build this however we like. Below the floor joists is a very shallow crawl space, dirt is only ~10" below joists. Insulation is between the joists.

The tub will be a drop-in on a framed deck, so it can be as high as we want it.

I am wondering if it would be preferable to install as much of the drain as possible above the floor, or at least above the rigid insulation we plan to put between the floor joists. (In other words, build a deck that is a bit higher than needed, and frame up the floor to support the mortar bed & tub.) If we installed it the normal way, directly on the subfloor, wouldn't there be a possibility the trap could freeze?

Also, assuming the tub is set in mortar bed, what is the best method for insulating it (when, with what?) It's bordered by two exterior walls.....

Thank you!