My baby is coming to 4 mths but we realise his feet are cold at night (if without socks on) even though he doesn't sleep in air-conditioned room. Is this common among babies or does it mean that his body is weak?

Don't worry, that's normal. My #1 always has cold hands n feet before he became more mobile (aft 6mths). Feel your baby's torso/body. If his torso is warm, your baby is ok! This is because his circulatory system is still developing, blood will go to the more important parts first :) His hands n feet will be warmer when he becomes more mobile n circulation is even out. If you are still concerned, there is no harm putting on a pair of little socks for him!