Beware, older languages below! The languages below were invented during Tolkien's earlier period and should be used with caution. Remember to never, ever mix words from different languages!

Qenya 

vanta-

verb. to walk, to walk, *trudge, trek

A verb for “to walk” in The Etymologies of the 1930s under the root ᴹ√BAT “tread” (Ety/BAT).

Neo-Quenya: For purposes of Neo-Eldarin, I assume ᴹ√BAT is for a “heavy walk” as opposed for √PAT for a “light walk” or “step”, so I would use vanta- for an extended or serious walk, and thus including “✱trudge” and “✱trek”.