Need lots more information.
1) what kind of plants?
2) when are you moving?
3) how far are you moving?

You may also want to try and ask on the garden/plant forums.

It depends on the moving company, the weather, & the length of time the plants will be in the van.

I'd bring it up when I interviewed movers.

If I were moving here in Texas in the summer (now to November), I'd sell them at a garage sale!

If you do move them, treat them the way mail-order plant sellers do:
water them well the night before, & pack them in boxes with crumpled paper for insulation & "shock absorbers".

Movers will not take houseplants! Most moving companies have a list of items that they will not move. Booze and houseplants are two I remember.Fireworks, paints, paint removers.........anything that can start a fire they won't take.
Certain states have very strict laws about the transportation of plants into the state due tho their heavy reliance on agriculture for their livelyhood.