Replacing 28in wheels with 26in I'm told that when touring (carrying a big load) you're much better off to have 26" wheels than 28". But most second-hand bikes seem to come with 28". 

Is it possible to replace the larger 28" wheels with smaller 26" ones?

What sorts of issues would I run into?


pedals hitting the ground?
v brakes not being able to reach tires? 
gear/derailleur issues?
etc?
It's possible to put smaller wheels into a bike frame but I can't see why you would want to. Bike frames are designed for a certain size wheel, so putting smaller ones in will affect the handling. 

You've already mentioned the brakes not working correctly, which is a fairly major factor. Pedals may or may not hit the ground, but you'd certainly have less ground clearance.

You haven't said why smaller 26" wheels are better. A bike with 26" wheels might be better for what you want to do, but just fitting 26" wheels to a bike made for 28" wheels is not good idea for the reasons above.

K