Is it normal to wear cologne to work?
Mostly.Normal for most people
Yes, wearing cologne to work is normal, as long as you keep it subtle. In a shared office, a little goes a long way.
Plenty of people wear cologne to work as part of getting ready. The main thing is keeping it light: you want coworkers to notice it only if they’re standing fairly close, not when you walk into the room.
Some people are sensitive to strong scents, and workplaces may have fragrance-free rules, so follow any office policy and ease up if someone mentions it. A small amount is generally fine; a cloud of cologne can be a lot for an enclosed workspace.