Ant beds around small trees.

I live and plant in a lowland area. When it rains the ants build up to escape the water level, which naturally pushes them towards my tree plantings which I've mounded up slightly during planting (dig a shallow hole, drop the root ball in. Cover with soil).

Should I worry about ant beds covering root collars? Their beds are sort of aerated, and I've had them build nests right up the plastic tubes which hasn't killed the trees. Yet.

If I should worry, what is the least effort for managing them? Vinegar seems to be the magic ant remover.

i doubt there’s much to worry about there. certainly not enough to pour vinegar in the root zone of your trees.

I agree with Greg, I would not put vinegar on the root zone.  Look around and I bet you can find their nest.

If you don't find the mound look for circle of different kind of dirt usually with a small hole.  Those are the places to use the vinegar.

for the most part, ants will not harm fruit trees at all, and do lots of beneficial things. unless you see actual damage or an issue of some sort, killing ant colonies is likely do more harm than good.

I have read the ants will not cross a  chalk line.
It would be worth a try hitting chalk over the ant nest, which is calcium.
I recently in my flower bed mixed a half a cup of blue down with a half a cup of baking soda and the rest water, of course 3/4 of the way full I shook it up waited on the bubbles to go down to finish filling and then check the top of the ant mount off with a stick and poured the mixture in. So far, no ants.  

This was in an area with flowers at this time but with all the rain it will not be long before it is washed deeper in the soil and I will put my flowers in.

I've had an ant hill severely damage the bark of an apple tree. The ants made a nest right beside the trunk and the mound came up maybe 6 inches. I checked it out after maybe a year and a lot of the bark touching the mound was rotting and sluffing off. Similar to burying a tree to deep.

While ants can and generally are beneficial, being so close to the tree will probably cause damage. The aeration is likely to cause patches of airpruning at the root. The their tunnels destabilize soil, which can lead to the tree leaning or being uprooted in a storm. I watched a colony of ants destroy the soil base of a new Japanese maple I purchased.  They thought my tree soil was ideal for their nursery.
Use a large amount of DE and poke it into the surrounding ant area with something non-intrusive like chopsticks.

Some ant species will help spread aphids, and protect them against other insects. Might not be a problem where you live, though - maybe the ants are not an aphid-farming species, or the trees are not susceptible to aphids, or you have aphid predators that are not really deterred by ants. I think it would be a good idea to leave them be for a while to see what happens, rather than using vinegar or some other poison "just in case".

It does depend on how far up the base of the tree they are going and whether they have earth piled up against the bark which can eventually cause rot.

I would observe over a period rather than getting rid of them as many ant species can be beneficial.

Only if you do see damage, I would use diatomaceous earth sprinkled around and in the main entrance hole and behind any loose bark, which will encourage survivors to move elsewhere.

I did a walkthrough today and the most vigorous of the grafted plantings (black walnut) do not have large mounds covering the root collars. I have acidic soil already, but might consider vinegar were the species acid tolerant. I'm not completely against commercial poison but overall I do not want additional inputs to the process, natural or otherwise.

For now I'm considering a 2 step approach where I simply press down the ant mound in the 6 or so inches surrounding the sapling. While doing so I noticed a lot more movement in the stem than I like and I do believe that the ant mounds are not helping the rooting and stability of the saplings. If regular compaction doesn't satisfy me later in the summer I will consider simply watering the area heavily to disrupt the colony. Neither approach would be feasible in a multi acre planting that I don't live adjacent to. Even on my 2 acres the watering would require jugs and a wagon, but this effort might be worthwhile in the heat of the summer.

Eventually I want to find a "do nothing" approach that is suitable for my climate so that I can keep up a large area with little help.

This was one of my first attempts at planting and I have since swapped to simply using a dibble bar as the digging and mounding is quite labor intense. As this doesn't create a raised safe zone during heavy rains I suspect the ants will not prefer those locations as strongly.

The dibble bar is worth mentioning twice. The dibble bar is not compatible with large root balls, however bareroot saplings have noteworthy upsides and the dibble bar has a poetry to the 3 movements needed in the simplest plantings. Bareroot saplings can be produced in large quantities from seeds and are cheaper when purchased. The only downside is being set back 2 or 3 years compared to planting a larger tree, but I'm young enough to believe I have the time and old enough to know that spending a ton of money for a quick garden of Eden fantasy isn't sensible. I'm excited about this approach for a scalable DIY propagation and forest planting, and will be posting more about this in the coming years I'm sure.

Now if you are in the tropics, ants can make it difficult to pick, prune and keep leaves on the trees (Leaf Cutter Ants. Many species can sting the bejeepers out of you, as well. Some ants species have a soldier caste with big jaws and I have seen them used in place of sutures: apply the ant while holding the wound closed, and after the ant bites the wound closed, pinch off the body, leaving the head and jaws in place until the wound is healed.