There's really no need to strip the mortar. You can "paint" the entire structure with an alcohol/india ink mix and it really won't change the brick color very much, if at all. I start with a very small amount of india ink added to the alcohol, then brush a small area. It it's too light I add another drop or two of ink, then brush again. Repeat until you get the desired effect.
You'll be happier with the results if you wash, prime, and paint the ice house first before applying the alcohol/ink wash. Use cheap primer and paint, preferably flat. I use the Walmart dollar cans. Use the same method as above to make the dirty wash. Don't use the same batch you mixed for the switch tower except as perhaps a trial. It may be darker than you want to weather the ice house.
There are many different ways you can weather a building. Peeling paint, rotted wood, and on and on. Here's a picture of a Bar Mills kit I did using only alcohol/india ink and chalk on the roof to weather: