No way would I have a hot tub delivered in sub freezing temps especially if it's sitting outside. The framing is not that strong. They're made to sit horizontally and can 'tolerate' some tipping and off-camber stress, but not much. The less the better. I've moved mine around a lot. Things creak and pop. Plastics don't like extreme cold temps and are highly prone to breakage and damage and there's a bunch of plastics on a hot tub. Guys bring them in and generally they've done several and can handle them with amazing efficiency, but once they are in place, they're gone probably to never return. What damage (if any occurred) are they going to see? Most likely you'd be ok if the handling was very careful, but do you think in below zero temps guys are going to inspect every square inch and look for potential damage? Of course not, it's TOO cold out!
Unless it was extreme damage it isn't going to be detected. As far as anyone knows, at the time of delivery, it was successful. If problems or leaks later develop, who's to say they weren't mfgr issues, or problems that occurred during shipping ...or handling? Of course the local seller will point back to the mfgr, otherwise it'll cost them money to repair. Besides the moving process, the simple act of removing the plastic side panels in near zero or below zero temps ....or any adjustments to the PVC fittings or pumps are all risking damage that wouldn't otherwise occur in warm weather. Just driving the side panel screws back in with a power driver can easily crack (split) the plastic panel board where it's thin at the top and bottom screws and it'll never be 'right' again. I would be most worried about the acrylic surface because if that gets cracked, then you're really screwed. They're never going to see a hairline crack in an obscure location in at or below zero temps. Personally, if I just forked out good $ for a hot tub, I wouldn't want one SINGLE item cracked or damaged which wouldn't have otherwise been broken. The potential risks are a lot higher. Why run the risk? Wait till it's in the 50's...