I would recommend against using it as a house gun, if you have other pistols.
Not for any of the reasons already mentioned, though.
First, if the gun checks out as mechanically sound, the age doesn't matter.
Second, there is no "self defense" ammo for the .32-20. A lead flat point bullet is nothing to sneer at, and put in the right place, it absolutely will work. I meant there are no JHP loads "optimized" for self defense in that caliber.
Even the "handgun" load .32-20 is the most powerful of the old .32 caliber pistol rounds, by a significant margin and also beats .32ACP. Original handgun loads were advertised as 1200fps, "rifle" loads were listed as 16-1700fps.
COWBOY loads are NOT the same. "Cowboy" loads are for playing the Cowboy Action shooting GAME. They are loaded very light (for least recoil) some people describe them as "cat sneeze" loads. Suitable for the game, and plinking, not a good choice for anything else.
And, just FYI, full power .32-20 loads are very LOUD from a pistol. I would not fire one inside a closed room, except in gravest extreme.
The main reason I would not recommend using your gun as a house gun is, if you ever DO need to use it in self defense, the police WILL take it. And, to them, it isn't a valuable firearm, its a piece of evidence. One they will keep until all legal matters are settled. This could be weeks, months, or possibly even years, and they are under no requirement to give the gun proper treatment or storage.
You will, eventually get the gun back, but it could be chipped, cracked, dinged, damaged or even rusted, which would be a true shame.
If possible get another gun to keep as a defense gun, one of lesser historical value. A modern .38 DA would do the job, and be easier to repair or replace if something should happen to it.