The rules are weirdly slippery on what a "solid surface" is.
Note that several "Wall of X" spells (ice, thorns, force) use similar language, as do monster attacks that create walls of stuff.
There are several cases of rules text using "solid surface" and "creature" as if they're distinct, which would imply that the surface can't be part of a creature. What makes it less clear is that the effect is usually the same either way, so "creature or solid surface" could just be inclusive language.
For example, the Otyugh can bash creatures "into each other or a solid surface", for the same amount of damage.
The catapult spell hurls an object in a straight line, "stopping early if it impacts against a solid surface." But if it would hit a creature, and the creature fails its Dex save, "the object strikes the target and stops moving."
You can break a Staff of the Magi "over your knee or against a solid surface"; the effect is the same, including the damage that you take for being in the center of the blast.
Melf's minute meteors is a tricky case. The meteor can be directed at a point you choose; it explodes when it "reaches its destination or impacts against a solid surface". This has a small functional effect: the meteors otherwise don't respect cover, so if a creature doesn't count as a "solid surface" then hiding under a big creature won't protect you from meteors coming down from above. Common sense says that it should protect you, so I lean toward "solid surface" being inclusive of creatures in this case.
So how do you rule on this?
One additional issue for the Wall spells is that "solid" implies that the surface isn't going to change shape during the duration of the spell. This matters mostly for Ice and Thorns, because they're rigid. If you cast a Wall of Ice on the back of a dragon, can the dragon shake it off? Does the wall flex as the dragon moves or does it splint the dragon in place? What happens if it tries to fly?
Another is that some of the walls do damage; if you allow a Wall of Fire to stick to a creature then that's 5d8 fire damage per turn, no save, for 10 turns.
Allowing walls to be used this way would introduce a lot of complexity that you might or might not want to deal with.