I'm curious how these beasts got down to the surface of Hoth.
Did the Galactic Empire land them in big ships, if so which ones?
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AT-ATs were typically deployed for ground assault from orbit by large dropships.
Walkers stationed within larger warships, such as the Executor-class Star Dreadnought, were delivered to planetary surfaces within Incom Y-85 Titan dropships, capable of carrying four 22.5-meter AT-ATs.
Smaller starships, such as the Imperial-class Star Destroyer, deployed single walkers via the Theta-class AT-AT barge.
- very similar to Y-85 as it was also made by Incom
Other designs, including the Telgorn Corporation Warlord Dropship, were capable of delivering a platoon of four walkers.
(Images courtesy Wookieepedia)
Since the commander of Blizzard Force, General Veers, served directly under Darth Vader and was a protégé of sorts, one can assume that the force was headquartered on Executor SSD - therefore the answer to your question as far as Hoth is Incom Y-85 Titan dropships.
This is confirmed by Hoth Battle Wookieepedia:
This mechanized force was deployed by several Y-85 Titan dropships, and larger landing assault craft. (src: Star Wars: Complete Locations).
The Rebels had to deactivate their shields so they could use ion-cannon to neutralize threatening Star Destroyers until shield would closed and transport would get rendezvous point.
Meanwhile Empire landed its AT-AT Walkers because they knew that shield was soon to be closed again and they could destroy the generator only from inside the shield.