If she is 4yrs now, you should be progressing with her training work. Under saddle or driven, whichever you prefer.
Being an all-arounder is a good goal for any horse, but some "work" may not be as helpful to go with horse's other jobs. Draft horse pulling of logs means that horse will learn to pull with the front-end, to get the load moved regardless of difficulties. The load MUST be moved, horse has to lay into the load to do it. You NEVER want a pleasure driving horse pulling with his front legs as he moves along! He needs to be "driving from behind" to get overstride and collection.
Has anyone in your family logged with horses? It is a skill that needs to be learned, taught, to avoid getting into trouble. Driver travels uphill of the animal so log doesn't roll downhill over them! Butt-end of logs and poles will snag while dragging, so you have to stop horse, move them over for pulling at a different angle. Snagging will stop load for a second, then log or pole JUMPS free with horse still pulling, can hit things or swing sideways to sweep you down. There is a real art to logging with equines. If the wood is small like fence posts, just a few, you might (after much practice with tires, NEVER TIE ROPE ONTO HORSE or saddle) try dragging them with horse under saddle. Wear chaps, that rope will put a hole in your pants leg fast.
Teaching a horse to drive is your time to put the basics on horse, voice commands, PROMPT response to a command. Using the whip for aiding the horse to bend or move FORWARD when asked. Horse has to get really solid out on the long lines before you try attaching any items to it. You have to build up the pulled loads slowly, make horse confident they CAN MOVE the load. Don't scare them with big loads first, they give up, go real stupid if nothing moves. Learning to move into pressure can take a while.
Some never drive, just don't have the mind for it.
Horse is a good age, should be fairly well developed with a mind that can listen and process what you are asking. Riding is fine first, long line work is still VERY helpful to horse in learning those commands, understanding what you ask. Get Whoa down VERY WELL. Should be a voice command, in case a rein breaks or gets dropped. Good solid Whoa is the best gait a horse should know!