I'm sure that the addition of trees being added to settlements has already been discussed, but I was thinking about ways they could be added and in a way that would make sense.

A couple of ways to start:

1. there is a faction in The Commonwealth that already has trees (likely everyone knows who, but to avoid spoilers I'll not name them), there could be a member of this group that could be looking to restore the environment of the world, and as such volunteers to assist settlements in growing trees (what if you are an enemy of this faction? the faction in question has had dissidents in the past and this person could be acting on their own accord).

2. starts when you ask a settler what you can help, they say they wish there were living trees. You have to hunt down botany and arbor-culture textbooks in ruined libraries, or get them from friendly factions.

further:

You build soil remediation and enriching devices, composting excess vegetables and organic waste. You then have to hunt down seeds, which could be stored in seed vaults or in seed storage areas of vaults. Along with seeds you'd have to hunt down in cold storage somewhere things like nitrogen fixing bacteria. trees would grow where planted, slowly over time, or could be FEV influenced and grow fast, but be a drain on your water supply while they do so.

more difficult to accomplish, but would really be interesting:

As the trees grow they could start to spread outward as the microbes you reintroduced to the soil also spread outward, making the soil habitable. it could be made to be the case that after a while (would of course be decades in real life, but can be accelerated for the game) you find the trees from settlements like sanctuary have spread down to the outskirts of Concord. trees as proposed would not spread to areas with detectable radiation and grow more slowly into urban areas so as to keep the world from becoming completely tree filled. They would be programmed to grow in such a way where they don't grow right on top of each other and also don't collide with other existing objects. Even smaller shrubs and grasses could start to make a come back and there would be more environments to explore over time, environments that you helped to create. To maintain the feel of the world there could be a radius to which trees would spread.

Great Idea.

I wish we could clone horses and chickens too.

You can't clone something that to our knowledge is extinct. At best they would be Synth animals like the Gorillas.

Really? I thought you could clone from DNA.

It would be so easy to make up a vault whose purpose was to store DNA and seeds for cloning whatever became extinct because of nuclear war, though.

So you want Bethesda to come up with some contrived reason to bring back two extinct animal species? That's not a good idea and it's terrible writing.

Also, The Vaults (Other than a few control Vaults) weren't mean to save anyone or anything. A cloning Vault already existed, adding another one would be pointless and quite frankly it wouldn't make any sense. Why would Vault-Tec have made two vaults that essentially fit the same purpose?

The seed vault could be one that was built by a company other than vault-tec. The alternate timeline of Fallout has other doomsday prep companies making things like Pulowski Preservation Shelters, there are companies in the real world that sell doomsday preppers heirloom seeds, it's conceivable that there would be a company similar to that in the Fallout universe.

Chikens and horses are just examples.

Contrived? You think it's unrealistic that a company or the government preserved flora and fauna DNA in case there's was a nuclear holocaust or other type of extinction level event?

That kind of stuff is already being done in real life. In fact, I think it would be weird and unrealistic that there wasn't such a place or places.

What would be so outlandish about finding a seed/DNA depository and trying to bring some plants and animals back to life?

It doesn't even have to be Vault tec, btw.

This.

To be honest, it would be unrealistic in my opinion if there wasn't some kind of seed and/or DNA bank out there underground somewhere.