2002 Chevrolet S-10 Antifreeze leak

I hope you mean that hose is above the transmission, not on it. If it's on it, and you have engine coolant coming out of it, we have bigger problems.

What I suspect you found is the AC condensate drain hose. It's about 4" long with a right angle bend, hanging down from the passenger side of the firewall under the hood. Coolant leaking from that is due to a leaking heater core. That's pretty common on GM vehicles and seems to be worse when the red Dex-Cool anti-freeze hasn't been changed. GM advertised it as "lifetime" coolant to make the cost of maintenance appear lower than that of their competitors. Then they tricked you further by sticking a label on the reservoir that says to replace it every three years. Even the Dex-Cool manufacturer says to replace it every two years because that's when the water pump lubricant and rust inhibitor additives wear out.

When the coolant isn't replaced often, acids build up in it from the normal seepage of combustion gases into it. Any time you have two different metals and an acid, you have corrosion, and that shows up mostly in leaking heater cores and radiators. You can actually test for that, but it works best if you have a radiator cap. GM saw fit to leave that off a lot of their vehicles. Use a voltmeter with one probe on the battery negative post and the other one dipped into the coolant but not touching any metal parts. The higher the voltage you find, the more acid is in the coolant, and the faster it will attack the new heater core.

Any chance you can post a photo of it? The AC drain hose is about an inch in diameter and the end is flattened to keep bugs and wind out. It's attached to the firewall. What is the hose you found attached to? The only other hose I can think of is a heater hose, but those are bigger, and if one is not attached on one end you'd have a major leak and the engine would overheat.