We used to have our own saddle stalls with mangers, saddle, and bridle racks at home.
Now we keep everything in the the tack room of our trailer....and on several racks in the house.
Same as the OP I have those 3 drawer plastic chests for polos, boots, extra chicago screws, tools, curbstraps, roping gloves and some vet supplies that don't fit in my vet box. My vet box(a tool box) is in the trailer, except for the meds that require the fridge.
I leave all my snaffle setups in the trailer on the bridle hooks but all the good bridles and hackamores in the house.
The pads and blankets I try to hang out to dry every time I use them then get hung on the blanket bars in the trailer..otherwise they get stinky and gross.
Since moisture effects ropes I try to keep them in the mud room and coiled nicely so they aren't too kinked and weird when we rope.
Because of the humidity, I open the door to the tack room everyday whether I ride or not to get air in there so nothing molds.