Quick question about medieval traveling

Probably a donkey cart to carry luggage/costumes/stuff. The rest of them walk.

Sounds like you need 'The Time Traveller's Guide to Medieval England' by Ian Mortimer

If your actors are particularly successful, a few of them may have received horses as gifts from wealthy patrons.

One sec--Don't buy Mortimer's book if you're looking for Tudor England, specifically--it's a fantastic book, but I just checked, and it's about the 14th century, specifically. Which is before the Tudors.

(I love Mortimer and it was my first thought too.)

Tudor England, technically, is Renaissance.

In English history the Renaissance is generally considered to start with the Battle of Bosworth Field, in 1485, when the Tudor dynasty started.

There would have been a cart, pulled by donkeys, or horses, a few outriders on horses or donkeys. The scenes with the players in Stoppard's film version of Rosencrantz and Guildenstern are dead is pretty much spot on--the "technical" advisers were Stephen Orgel, among others.