There is no definitive answer
As written there is nothing to say whether or not land vehicles should be included (or excluded) in the effect of Elk totem option for the 6th-level Aspect of the Beast from the Barbarians Path of the Totem Warrior. (SCAG p. 122)
Elk. Whether mounted or on foot, your travel pace is doubled, as is
the travel pace of up to 10 companions while they’re within 60 feet of
you and you’re not incapacitated (see chapter 8 in the Player’s
Handbook for more information about travel pace). The elk spirit helps
you roam far and fast.
My personal interpretation of the RAW would be to allow basic land vehicles (Carts, Wagons, Carriages) to be included in the effect as long as all passengers in said vehicle are included in the effect, are within range and don’t exceed the companion limit. This could be interpreted as a form of mounted travel.
Part of this interpretation comes from the fact that in 5e, there is only a single table for travel pace that applies to all modes of travel. The only benefits to mounted travel are the ability to gallop (a short speed boost that exhausts the mount after an hour of travelling at double speed) and increased carrying capacity. A vehicle only further increases the carrying capacity of the mount.
The reason I would limit it to basic land vehicles is that both water and magic vehicles are not pulled by mounts (in most cases). If you are Captain Jack Sparrow riding on the back of a sea turtle an exception could be made.
An explicit ruling may be needed for the case where part of the conditions are not met, no one benefits from the effect when passengers are involved.