Big. Whatever Raspbian can read.
I have used 256 GB memory sticks, and 2TB Samsung T5 bus powered SSD without problem (also a smaller but faster 512 GB Samsung T7 SSD).
Whenever in doubt, just check Raspberry Pi 4 and Raspbian for the ASIAIR capabilities, since those are what the ASIAIR is based on.
One thing to be mindful of is that devices and connectors that are sold to consumers may not work well below 0ºC (what they are usually spec'ed for).
The Raspberry Pi itself can tolerate low temperatures a bit better because of internal self heating. But things like USB connectors and USB memory (and any USB device that does not generate enough self heating) may not fare so well under low temperatures. If funny glitches (devices starting to drop out, for example) start appearing when Winter arrives, you will know what to look out for, especially with things exposed to open air.
Watch out especially for connectors that are not strain relieved or taped tightly so there is zero movement was the telescope moves through the course of the night.
My ASIAIR is inside an enclosed waterproof box together with an eero router, which also generates a lot of heat (the two together generate about 10 watts); the box is a few inches off the ground at the base of my tri-pier). My 256 GB memory stick is also inside the box (accessed through the Raspbian Samba server, so I need not open the box normally) and does not become as cold as if it were exposed to open air.
Chen
