In the books (not in the film) between Shire and Bree, Frodo and hobbit fellows met (before or after Tom Bombadil I can't remember) a group of Elves. Their leader told them he could try to offer protection from Nazgul, if he would have a battalion of elven archers like ancient times.

According to Silmarillion, Elves lived in open fields, in strong castle cities as well as forests. Tolkien does not classify them specifically as "wood elves", neither tells that Elves always lived in the forests. But at the time LoTR takes place, Elves are weak in numbers and civilization, and therefore they prefer hidden in the woods.

But there are enough number of references in the books to make us sense that bow is a preferred STANDARD weapon for Elves, no matter where they used to live.

Immortality is related to that preference not only for personal choice. As an immortal race, Elves also are rare, and most of times been, outnumbered, and strategically more limited in "casualty rates" therefore it is more costly for them to lose their members. A successfull use of ranged weapons in correct combination, is the safest way to minimize casualties, given that you have much better archers in mass scale.

Any member of any race, who can masterize bow skill, would go after it. (Humans and Orcs have also specilaized ranged untis) However, Elves as a society, have more reason, more ecological pressure, and have more resources (time,material,skill etc) to make bows standard combat weapon, no matter how good they are at other weapons.

I don't share the opininon that Elves "small size" is a point. Longbows require pulling strength, and archers in real history, are certainly big, tall, strong men, who were also very strong opponenets in close combat, often deadly with a crude melee weapon, a dagger, an axe or hammer. Close combat specilization does not require "more body and muscle mass" than archery, but simply different tactis, equipments and skills.

In real history, bows are really most skill dependent weapons. Actually, the reason why bows dissapeared from battlefield, even before modern rifles became so accurate and deadly, is the problem of training time. You may train a bunch of peasants for a few months to have a standart unit of musketeers. An archer who can use a long bow (composite or non composite) effectively and safely in battle, requires a training of 10-12 years at least, and a "sea archer" or a "mounted archher" cannot become even good enough with the weapon before 20-25 years. Lost musketeers can easily be replaced, whereas, lost archers cannot. (Ottoman archers were expected to "pull the string and set the bow" to develop strength and understanding of the limits of the bow, string, and their arms. They were not allowed even to shoot an arrow before they advance a few years in their initial training.)