Hello, I'm new to the forums as far as posts are concerned. I have 95 s10 4.3 v6 and my heat is only blowing out of the defrost vent but ac blows out of every vent. I read online to check the hoses in the engine when I found a small broken hose under the battery. Does anyone know what this hose it?

 

Looks like a vacuum hose that leads to or (any vacuum leak does) has an effect on the HVAC (Heating, Ventilation and Air Conditioning) in the cab.
It may splice off to a tee or have the tee incorporated, but that looks like the issue for the HVAC.
A broader pic may help if you can still circle the issue hose.

 

Here is a wider view of the

engine

 

That looks like the vacuum line for the 4wd actuator.
There should be another hose that size somewhere around there.
Hook up the hose to that fitting.
Bet you don't have 4wd working either.

 

The other hose is under the battery but as far as I know my 4wd works I periodically do short test where I turn on 4wd for a block or two to make sure it wont break but I haven't checked it on a month or so.

 

Rotti is correct. You may think your 4x4 is working but bet you a buck its not. You will get stuck next time you need it. You will here the transfer case motor work and the gears will drop into 4 low but your front axle will not be locked. I have a 95 and those are the only vac lines that are there. It runs down by the distributor under the firewall to the three vac line transfer case switch. When that switch goes you will get fluid in the 4x4 actuator and your HVAC vac actuators and that can be a real mess.

 

Yeah hitting the button & the 4x4 lights up doesn't mean it's working. Put it in 4x4 & find some sand or loose gravel & haul on it, do just the rear tires break free or do you have torque steer? Meaning the front diff is engaged.
spitty is right about the switch & getting fluid into it, a PITA for sure cleaning out the lines & the cost of a new switch.

 

Would I need new lines and a switch, or replace the the broken hose and then test the 4wd hi and low and see if it works?

 

Go the easy route - replace the line & then see if the switch/actuator is working or not.

 

On vac lines the ones that decompose the fastest are the ones exposed to heat in the engine compartment. The ones that go back over the tranny in genral hold up pretty well. What I did with mine was cut out all the stuff foward of the firewall splicing to the better condition lower ones with hose barbs. Take the battery and tray out and see if there is any fluid in the vac actuator. If there is you will need to replace the transfer case switch ASAP.