Most lawn furniture can be carried and moved as is without any padding because it’s built for scuffing in the outdoors.

Some very expensive things should be well cared for with padding, however, such as the table pictured below.

Umbrellas should be closed, of course, and then wrapped in a pad which can be taped to hold it shut. Lawn furniture is normally loaded last on the truck and kept separate from inside furnishings because some of it may be dirty.
Playhouses
Yard playhouses normally are so big that they must be disassembled for moving and then reassembled in the yard of the new residence. Sometimes, however, they are small enough where they will fit in the truck on a separate trip. In some cases, when a truck with a tailgate or a lift gate is being used, the playhouse can be set out on it and strapped to the back of the truck. In that case, hang red flags off of the back of it to signal other motorists of your oversized load.
Then drive slowly and carefully and watch your truck’s rear end swings to be sure you don’t hit something with it when you make a turn. If the playhouse is higher than your truck, watch the height restrictions of viaducts and overpasses. If it is wider than your truck, have someone follow you and stay right behind you with a wide load sign in their rear window to signal other motorists. Whatever you do in this circumstance, police or a sheriff may stop you and ticket you for some local violation or infringement so check with them first for permits before proceeding.
Moving outdoor furniture can be a tough task for you alone. If you get stuck or you don’t think you can handle the outdoor furniture moving job at all, then get a quote from reputable furniture movers to guarantee the success of the entire relocation business.