They always leave open ended hoses pointing downwards to stop dirt or splashed water getting in.

 

Quadcrazy has a good selection of manuals, or ManualsLib.

I should probably mention that some breather hoses do dangle down open ended, or sometimes with a sort of lipped one way valve to keep dirt out, but in both case not connected to anything.
It's common to have breathers come off the tank, carb, axle housing etc and go up above any intended water line, and then back down to dangle open to the atmosphere. The ones going into the carb and engine though, because they are crucial, and because they will develop vacuum when the cold water cools the engine, often have a branched off hose going to some restricted vent to break the vacuum and prevent the crankcase or carb filling with water. That branched anti-vacuum hose sometimes goes to the air-filter housing.
Hope that helps you figure it out. The honda manuals have pretty good diagrams though and if you study the plan and side view diagrams you should be able to figure it out. If it's not clear in the diagrams, read the notes and/or refer to the fuel section where it might explain any details..

 

Thanks brother! I appreciate the information and advice. I found a Honda manual and it looked like the branch hose went up towards the gas tank area and was left open ended. I tried locating that exact area after pulling off the outer plastic side plate yet didn’t see that particular spot, or what the manual showed as a clip to hold it in place. I decided to run it up that same route and tucked into place to where it wouldn’t dangle and left it open ended. I have a local ATV mechanic I hope to eventually run it to to have him look at it…as a double check.

 

Thanks brother! I will give that a try.

 

If you download a genuine honda service manual it will have a wiring, cable and hose routing diagram.