Placing a water heater outside?

[Thomas Kim]

I'm in the process of building a small laundry room (approx. 10' x 10'); however, the water heater is currently in the corner of this space taking up 2.5' x 2.5' of space. I was told by a plumber he could remove the traditional water heater and put a tankless water heater outside; thus, it would open up that 2.5' x 2.5' space for more room.

My question is rather than paying $1k+ for a tankless water heater, is it safe to just move the traditional water heater I have to the outside, but enclosed in a wooden "shed"? Or is my only (safe) option to get an outdoor tankless water heater?

Thanks in advance.