Смотря в какой поход - есть несколько разных значений:
https://www.lingvolive.com/ru-ru/translate/ru-en/поход

Передвижение войск: We're going on a march tomorrow (?)

Uly,
In Russian, «идти/ходить в поход» usually means to go on a hike in a natural environment like a distant forest or a lake, opposed to a city excursion. People are equipped with a stuff like backpacks with food, mats to sleep on the ground, tents etc. Is there a specific term for THAT kind of hike in English?

Like an overnight hiking trip?

Yep. Or for a whole vacation or longer.

So a hiking trip?

Looks like that.