Does a private backyard surrounded by trees (woods) require an eruv?

Shalom, Thank you for your question. A private yard can sometimes be considered as completely enclosed which would allow carrying in it, and from the house to the yard and back. In order for this to be the case the yard would need to be almost totally surrounded by fencing (or a series of posts and lentils – which have many technical details that need to be considered). In your case we would first need to examine if the trees (the woods) are close enough together to be considered as a “wall”. This is the case if there is no space more than three “tefachim” (about 24cm) in the “wall” of trees. This is somethings the case with a tight hedge that starts at ground level and is at least 80cm high. However, it seems unlikely that if your garden just ends in the start of the woods that the trees are going to be close enough together to be considered as a “wall” that allows carrying. It is possible to build an eruv around most private gardens – but you would be best advised to invite a learned Rabbi over to give you advise on site as to how to do so. Blessings.