Phrases like: "he is surrounded by..." always seem to be translated as: "er ist von .... umgeben". Does a passive construction like : "Er wird von Bäumen umgeben" sound strange (Or wrong) to native speakers?
A sentence like
Das Haus ist von Bäumen umgeben.
is passive, but Zustandspassiv.
Zustandspassiv is used to describe a state, whereas Vorgangspassiv (with werden) is used to describe an action.
Because umgeben describes a state rather than an action, Vorgangspassiv doesn't fit well, so Zustandspassiv is preferred.
There are two ways to form a passive construction; these are exactly the two you use in your question. However, the meaning and implication is different. Because your example using trees does not fit absolutely perfectly semantically (it is still possible but somewhat less likely) let me use a slightly different example where the surrounding thing are troops (Truppen)—something generally considered to be mobile.
Er wird von Truppen umgeben.
This perfectly normal and idiomatic German sentence does not mean that he is surrounded by troops. Instead, it means he is being or he will be surrounded by troops. It is called the Vorgangspassive (dynamic passive). A typical situation could be the generals sitting together and planning their siege that will start tonight (‘will be’) or an observer watching the troops slowly and silently surround him, wherever he is. The key element is the movement: there is a before and an after; there are no troops surrounding him before but there are afterwards.
Er ist von Truppen umgeben.
This perfectly normal and idiomatic German sentence does mean that he currently is surrounded by troops. It is called the Zustandspassiv (stative passive). A typical situation would be an observer coming to the scene of the siege when all troops are already in their positions and waiting for their next order. There is no implication of how long this situation has been going on for—it could be seconds or months—but the fact is that they are there. This is also the key element: the static presence. There is no before or after, just a now.