There is only one RAW answer I could find for a 5e land vehicle. In the DMG page 151 there is a Apparatus of Kwalish (called Apparatus of the Crab in the SRD page 208) which is described as a 2-person 20 AC 200 hit point vehicle that transforms out of a barrel. Unfortunately, the stat block isn't filled out as much as the DMG page 119 table is filled out for air and water vehicles.
Speaking of page 119 of the DMG, for an RAI answer, there is a Jeremy Crawford tweet about creating stat blocks for vehicles that references this table.
Wolf Hunter @WolfHunter83
· Jun 3, 2015
@JeremyECrawford If I wanted to design new vehicles, how could I determine HP, AC, Damage Treshold and similar factors?
Jeremy Crawford @JeremyECrawford
@WolfHunter83 I'd pick a vehicle (DMG, 119) that's close to the size I want and then reskin or tweak it. No need to do extensive design.
I think this gives you the RAI direction to reskin something like the keelboat to a carriage, for example.
If you're looking for inspiration, there is a 3e reference book Arms and Equipment Guide which does have full stat blocks and details for many land vehicles. I'm not personally familiar with the book, and I found that reference in a related 3.5e question also asking about vehicle stats. Granted, the stats don't compare to the air and water vehicles from 5e. Here is a quick snip for the cart from 3e:
Cart: Large vehicle, 30 hp, 5 hardness, 4 AC...
If you want to go for converting 3e there is a DnD Conversion reference. Although -- vehicles are such an edge case -- I think you'll be better served by reskinning the water and air vehicles from 5e.