"The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized."
"Effects" essentially means "belongings" or "personal property" or "stuff".
So while the tent isn't a house, it's a container of your stuff, and looking inside it would be equivalent to looking inside a backpack.
There are exceptions to the 4th amendment, like if an officer hears a scream for help, or if the officer sees you carrying and sees you throw the gun into your tent. But for the most part, your personal effects are protected from search unless you consent.
I'm not a constitutional lawyer.