I have tons of large branches that have fallen on the ground near the pond. I don't want to just leave them there because I will have to mow soon and the lawnmower doesn't agree with large branches. These branches are medium sized in terms of thickness and length (approx 3 inches thick and 8 feet long) so they're not suitable for turning into cords of firewood.

Here are the options I have thought about:

1. Throw them in the pond to create habitat. Pond already has lots of plant growth and fallen trees that already provide habitat, so I don't really think this pond needs more habitat. The only exception may be the deep area in the center which is approx 12 feet deep. Does it make sense to dump large tree branches and create habitats in deep water?

2. Burn it

3. See if somebody wants to come out and take it for free, maybe they use it for other wood products besides firewood?

4. Haul away to a dump/landfill site

Brush piles on dry land make great wildlife habitat. Just build them where you don't mow.

https://www.extension.iastate.edu/smallfarms/wildlife-shelters-brush-piles-and-predator-excluders

Very good article on the value of brush piles RAH. Thanks for the link.

I have built several piles on our wooded 3 acres. It is advised to support the brush rather than place it directly on the ground. I've laid a couple of logs 6" to 12" on the ground, then built my piles on top of them.
I've also set cinder blocks on the ground, placed pallets on the blocks, and then the brush on top of the pallets. This keeps an open but protected space under the brush rather than allowing the brush to collapse onto the dirt so tightly no critter can get under it.

In many years of pursuing upland game, I remember pheasants, ruffed grouse, and of course cottontail rabbits flushing from brush piles.

Once upon a time, I burned brush piles, but not anymore.

If you have enough...build the brush pile/s. I have started brush piles using discarded/broken pallets. Lay the pallet down and pile the brush on. The rabbits sure like them and that was my goal.

Deep water habitat has it's place and more so with aerated ponds, but I would not add 3" minus limbs to deep water and I would hate to have to try and weigh it down properly if the pond already has water in it.

If brush piles are not really an option, a fire can be nice on a spring evening with a guest or two. Turn the chore into and event! Alot of people maintain a fire ring (of rocks, or man-made steel, etc) just for the occasional burning of lawn refuse and such.