Learn Swedish: Vi går ut genom grinden. - We go out through the gate.

Genom translates directly to "through" and is used to describe the path or trajectory of a movement from one side of something to the other. Here, the gate (grinden) is the physical threshold you are passing through on your way out.

I always mix up ut and ute. Why is it ut in this sentence?

This is a great refresher on direction versus location! The sentence describes movement toward a destination, not a fixed position. Ut means "out" (direction of motion), while ute means "outside" (already being there). Since you are actively moving (går), you must use the motion word ut.

Could I just say Vi går genom grinden without ut?

Yes, you can! Vi går genom grinden simply means "We walk through the gate." Adding ut just provides a fuller picture of the action: it emphasizes that your overall goal is to go outside, and the specific path you take to get there is through the gate.

Is en grind the same thing as a door?

Not quite. En grind specifically refers to a gate in a fence, wall, or hedge outdoors. A regular door in a building is en dörr, and an airport boarding gate is usually just called en gate in Swedish.