To illustrate the situation in a more relatable way, I have a lvl 3 halfling drakewarden ranger who wants to circumvent the whole "it only becomes a mount at lvl 7" argument by hitching it to a rickshaw, as shown:
I could not find anything mentioning if a wagon (or in this case, a chariot would be the closest equivalent) could be pulled by a small-sized creature, but I did find the Lifting and Carrying section of D&DBeyond quite interesting:
Carrying Capacity. Your carrying capacity is your Strength score multiplied by 15. This is the weight (in pounds) that you can carry, which is high enough that most characters don't usually have to worry about it.
Push, Drag, or Lift. You can push, drag, or lift a weight in pounds up to twice your carrying capacity (or 30 times your Strength score). While pushing or dragging weight in excess of your carrying capacity, your speed drops to 5 feet.
Size and Strength. Larger creatures can bear more weight, whereas Tiny creatures can carry less. For each size category above Medium, double the creature's carrying capacity and the amount it can push, drag, or lift. For a Tiny creature, halve these weights.
If I am reading this correctly, the carrying capacity (mount) of a creature would be the drake's strength (16) times 15, so 240 lbs (which is already enough to carry him, but still). However, when tied to a land vehicle, the drake's weight limit would then double to 480 lbs, which would be strong enough to carry possibly 2 adventurers.
Am I reading this right, or did I miss something?
As an aside, if my understanding is correct, that would suggest that the 12 rhosgobel (almiraj STR 2) that pulled Radagast's sled would be able to effectively pull 720 lbs, minus the 300 lbs sled, so in effect still be plausible both in reality (cause those weren't CGI hares) and in D&D... that is as long as they don't need the "mount" tag...