I really love steam engines that pull tenders with a doghouse on them. But what is their purpose?
The purpose of a dog house was to provide a seat an shelter from the weather when a third seat was not available inside a locomotives cab.
Why do only a few tenders have them
Most road locomotives had a seat in the cab for the head end brakeman.
most importantly, what's inside the doghouse?
A seat for the head end brakeman. 
Hot Water pointed out that
Some states, back in the day, had a more aggressive "full crew law", which required an additional Brakeman (sometimes positioned on the headend and sometimes in the caboose).
Here is Washington State law from the 1950s.
It shall be unlawful for any . . . corporation . . . operating any railroad . . . in the State of Washington . . . to operate over its road or any part thereof, or suffer or permit to be run over its road outside of the yard limits, any freight train consisting of twenty-five or more cars exclusive of engine and caboose, with less than a full train crew consisting of six men, to wit: one engineer, one fireman, one conductor, two brakemen and one flagman . - See more at: http://www.atg.wa.gov/ago-opin...sthash.pzPznNgD.dpuf
And here is where each crew member would normally ride on the train:
Engineer: Locomotive Cab
Fireman: Locomotive Cab
Head Brakeman: Locomotive Cab or Doghouse
Conductor: Caboose
Rear Brakeman: Caboose
Flagman: Caboose
Before radios the head brakeman and the flagman had the critical duty of walking ahead of and behind the train with their flag, fusees or lantern and track torpedos to protect their train if it was stopped on a main track that it did not have authority by time table or train order to occupy. This could happen for any number of reasons.
If an air hose failed, sending the brakes into emergency and stopping the train, it could cause a delay in clearing the main line for a superior train. The head brakeman and flagman would head out to protect the train as the rear brakeman and conductor fixed the problem. When the conductor notified the engineer that the problem was fixed the engineer would whistle in the flagman.
All of the men in train service might also be needed to pass hand signals to the engineer if the train was long enough to prevent the engineer from directly seeing a brakeman who was coupling or uncoupling cars away from the locomotive. Curves and line side trees or buildings often made this necessary. Standing on car top running boards to pass signals was common.
Radios, especially transistorized portable radios, have made railroading more efficient and much safer.
