Does surprise arrest existing movement?

Question

Do surprised creatures which were already moving prior to being surprised keep moving, or stop moving for a round?

Some illustrative situations might be:

• A carriage drawn by four horses is heading down a road at 60 feet/round. The carriage is ambushed by previously unseen goblins, and the driver and horses are Surprised. Does the carriage stay exactly where it is on the round they are all surprised, or does it continue 60 feet in the direction it was going?
• PCs cast Gate on a dragon rider mid-flight. The rider is drawn through the portal. Their dragon is Surprised. On the round it's surprised, does it hover at the position in the air the Gate is, or does it continue flying?

Answer 1

RAW: Yes, and that's fine

The relevant excerpt from the Player's Handbook (p. 189):

If you're surprised, you can't move or take an action on your first turn of the combat, and you can't take a reaction until that turn ends.

Which would mean a creature which for whatever reason was moving before Initiative was rolled, does not move during its first turn (the turn on which it was surprised). This might seem odd at first, however, it is an artefact of what initiative order, and surprise, is trying to emulate.

The typical scenario is one party (the aggressors) initiates on another party which did not know about them. The aggressors have the opportunity to choose exactly when they attack, and so have one round (a span of 6 seconds) to act before "normal" combat resumes.

Let's use the moving horse and cart as an example. The aggressors decide to attack as the cart passes them as so Initiative starts with the cart by the party, surprised and "stationary". The alternatives to using Initiative/Surprise in this fashion leave the success of such ambushes up to the Initiative roll. For the dragon example, the casting of gate should happen on the first roll of initiative. Otherwise for much the same reason.

The key is that residual movement of the first turn of initiative is abstracted away, such that the creatures are during that round where the aggressors wanted them for their planned attack. As a more general note Initiative, Turns and Rounds should not be considered too closely. Everything that happens during a round is narratively happening semi-simultaneously during the span of 6 seconds. This is a way for a game to handle that.

If you would like to have a cart continue moving even though they (horses, drivers, the mimic under the seat, etc.) are surprised, that is doable, just make sure it does not break the ambush that is planned. The aggressor has the agency to strike precisely when they wish to, and so should be able to start initiative as is most convenient to them. There is so much DM fiat in when to roll initiative and who are surprised, that minor modifications like this should not be an issue.

Answer 2

Generally speaking, while in initiative order, creatures do not move when it is not their turn

Before I continue, I just want to make sure it doesn't go unstated that there are obvious exceptions:

• Using the Ready Action and choosing to move when using their Reaction, instead of taking an Action
• Being moved by an external force, like a spell or someone using the Shove Attack Action (possibly relevant!)
• Otherwise have a feature that causes them to move (maybe a boss monster's Legendary Action?)
• Possibly some other specific circumstance

But setting those exceptions aside, a creature should stay in place until its turn begins.

So if a creature is surprised (or enters combat normally!), it should generally not move anywhere until one of its turns comes up while not surprised. If a creature is moving when it gets surprised, then it stops moving until a non-surprised turn comes up for that creature.

This makes sense: Surprise is generally an abstraction for a group of creatures getting an extra chance to get some damage in before anyone on the receiving end has had a chance to react. It might seem weird for the cart to stand in place for what is nearly 6 whole seconds, but that is the nominal benefit that Surprise is supposed to confer.

Alternatively, there's ways to work around this if, as DM, you don't like this mechanic.

Alternative: The horse-drawn carriage

Any time I'm dealing with a vehicle that is, in Principle, autonomously driven—I would nominally consider a Horse-Drawn carriage to constitute as such—I usually just assign it an Initiative Order of 20 or 1, and have the vehicle (and anything/anyone on it) move X feet on that initiative count as a Lair Action for this encounter.

^{If you're unfamiliar with Lair Actions, I suggest looking at some of the Boss-tier monsters in the Monster Manual, who often have Lair Actions that occur at specific initiative counts, usually 20 or 1. For example, see the Ancient Black Dragon, on page 87 of the Monster Manual.}

So in this case, I might cause the carriage to move forwards at its listed speed every time the Initiative count reaches 1. For the creatures that are Surprising the cart, this gives them a chance to

• Attack the wheels, slowing or stopping the carriage
• Attack the horses, injuring them or causing them to break free from control
• Climb onto the cart, so that it moves them with the cart

All of which give them a chance to take actions without artificially interrupting the movement of the cart.

The Dragon Rider

In this case, the dragon is usually considered the "Mount" of the creature who was riding it; its initiative would be the same as the rider, and occur right after it in the Initiative Order. The dragon would be frozen in place for the turn it is surprised, and remain there until its next, non-surprised turn comes up. You could apply the previous rule I suggested to the dragon, but given the dragon is (I'm assuming) a sapient creature, it's probably better to just apply the normal rules for Surprise.