The standard map scripts usually don't allow tundra in the starting BFC of a civ. Any tundras will be changed to plains or grassland. This means a deer at the start is always a plains deer. They won't be forested though, and I've never seen forest grow onto one either. But this is probably because I usually put a camp up early and forest won't grow on improvements. Apparently forest can grow on resources where it is allowed to grow. Some mapscripts allow even forested plains deer in your starting BFC. Together with settler on PH, this is quite a fast start. With settler on stone/marble PH, you could get a 9 turn worker.