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 Wookiepedia)
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 Wookiepedia:
This mechanized force was deployed by several Y-85 Titan dropships, and larger landing assault craft. (src: "Star Wars: Complete Locations").
They landed outside the shield then walked through. Once they destroyed the generator the general told Darth Vader that he could land.
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.
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