Yes.

(The "Trojan Horse" as we know it from the Homeric epics and other legends of the Trojan War is, like many elements of those stories, pure fiction. There is no historical evidence that Mycenaean Greeks--or anyone else for that matter--ever hid soldiers inside a giant wooden animal to sneak into an enemy town. Any discussion about a "Trojan Horse" needs to start with this acknowledgement. But let's leave that aside, because the question isn't did the Mycenaean Greeks build a "Trojan Horse," but could they have.)

We can break this question down into two sub-questions:

- Could Mycenaean Greeks build a large, hollow structure out of wood?

- Could they put that structure on wheels capable of holding its weight?

We can answer the first sub-question easily because there's a simple analogue: ships. Mycenaean Greeks were skilled shipbuilders. We know that Mycenaean kings traded as far away as Egypt and Italy, and ships feature in Mycenaean art. The Uluburun shipwreck found on the south coast of Turkey dates from the Mycenaean period and gives us a good idea of how ships of the period were constructed. (The personal gear of the Uluburun ship's crew shows connections to the Levant and suggests that the ship may have been built there, but Mycenaean ships were probably quite similar.) There is no doubt that Mycenaean carpenters were quite capable of building large wooden structures that could hold multiple people.

The answer to the second sub-question is a little less definite. We know that Mycenaean Greeks used chariots, carts, and other kinds of wheeled vehicles. There is no evidence for a Mycenaean cart quite as large or heavy as the imaginary "Trojan Horse," but the principle of putting a thing large enough to carry people on wheels was well known to Mycenaean crafters. During the Mycenaean period, the Assyrian Empire was making big advances in siege technology, creating battering rams, siege towers, and other large, heavy machinery that could be moved across a battlefield on wheels; it would almost certainly have been within the technical capacity of the Mycenaeans to do the same. (In fact, some historians have speculated that the "Trojan Horse" legend may have come about as someone in the Greek world who didn't really understand siege warfare tried to make sense of hazily-understood rumors about battering rams and siege towers: i.e. large wooden things on wheels that one army could use to get behind the walls of another.)