Those arrows in the road are called Brake Line Arrows and warn if you are approaching a corner too fast. It is a color-changing guide on the road, showing when to brake or slow down: green means you are going at a safe speed, yellow signals caution (you may slide a bit in the upcoming corner), and red urges braking before the corner, or you will crash. Practice cornering to master this very important skill in the game! You won't see these arrows in the road in Workouts as you cannot crash and your focus will be on your physical workout, instead.
Configure Brake Lines to be Off/On in Settings (Shift+Q > Assist). The default is On. You can also set how aggressively you brake in Auto Brake: Off, Moderate (default), & Aggressive (ESC in game > Assists upper right). Search the FAQ named "What is Auto Braking?" for information on how to set your braking.