I watered my orchids with water that was likely too cold. What kind of issues can I expect?

Probably nothing. My tap water is this temperature in the winter, and I've watered my plants with it before, no damage.

 

I think we'd all just be guessing here, there are too many factors to consider. You'll want to keep an eye on things obviously, but I doubt those temperatures are going to kill anything outright.

If there's going to be damage, my experience is that the first effects will be seen in the root tips. If there were any actively growing root tips that got too cold for too long, they may go dormant or even dry up and die. I think that would happen within days or less of exposure.

Keep in mind, Phals are generally hot growing orchids, yet some folks swear by the "just add ice" method for watering them. I'm pretty sure the water from melting ice is going to be at least as cold as what you're describing, and many orchids are more cool/cold tolerant than Phals.

 

For years, I let the RO tank in my greenhouse be whatever it was, based upon the greenhouse air temperature. NB: it will be cooler than the air temperature, courtesy of evaporative cooling.

I didn't notice any particular issues with the plants, but later, after immersing an aquarium heater in the tank, keeping it at 75F, I saw that plants that had routinely shut down all growth over the winter just kept on growing and blooming.

Be aware the some plants will suffer from mesophyll collapse if their leaves get hit with cold water, particularly if they have been warmed by the sun.

 

I used to keep an aquarium heater in my RO tank, but it eventually failed by splitting open, and releasing the oily heat transfer medium into the tank. What a mess to clean up!

Moral, keep an eye on your heater.

 

Or buy one that's stainless steel instead of glass...

 

Or plastic, I suppose.