You cannot change your look while you are IN an activity, but you can customize it either before or after from the Home Screen by going to My Stuff > Garage. There, you can customize your Bike, Kit, or Avatar.
In the Emotes tab, you can select winning, losing, or special emotes. Winning and Losing emotes trigger automatically at the end of an activity. Special emotes can be deployed by holding Shift + the number shown in the Power Up Holding area (e.g., Shift +2). Enjoy adding some flair to your rider!