If your username (with garibaldi) implies your location, you might be referring to the hot springs near Whistler -- one of my favorite winter vacation spots, and I would never hestitate to go in the springs!
You can relax. There has never been a known case of herpes transmitted through water. Not because of disinfectants, but because of dilution etc -- simply not enough virus once diluted in all that water. And even plain water may disrupt and damage (and perhaps kill) HSV.
You are overreacting about hot springs. Warm water without distinfectants can become loaded with infectious bacteria, such as pseudomonas, which can cause a superfical skin infection ("hot tub folliculitis"). In my many years of professional public health experience, I've never heard of this happening in natural hot springs. Unlike hot tubs, there is continuous water flow, so I doubt bacteria could grow to high enough numbers to be a problem. I would guess the operator's warning is a health department requirement that doesn't necessarily reflect a particularly high risk.
Herpes blisters and sores may itch and burn, but herpes doesn't cause itching or burning without visible lesions.