My practice space looks like a practice pad on a stand, next to my drums, where I do rudiments and such while the tv is on, sometimes with youtube videos.
I feel very lucky to have a place where, besides heat, climate is not an issue. It sounds like, based on your situation and location, you want to get a dehumidifier, as noted above.
As for sound absorption, you could do a lot with DIY bass traps and such, but sound transmission can be a tough thing to mitigate. What's above/around the room where you play? How many windows?
It's a ground floor room with a picture window behind it and a picture window on the other side of the room. Above is ceiling and second floor is bedrooms. I like the idea of a humidifier in the basement. The cinderblock foundation is high enough that I could perhaps build some sort of smaller room down there. The basement walls would be ideal to help block out some of the noise. I have three pillows stuffed in my bass drum which has helped.
I want to take the pads off the drums sometimes to practice on the kit or the snare to make sure my technique is consistent. I've been practicing on different surfaces, practice pads, pillows, those rubber drum pad mufflers and a mouse pad on a table top and each surface has a different feel. I had a recent left hand injury which has healed and I had to switch over to traditional grip, (I really like this drip!)...so the different surfaces really test to see if I am consistent in technique (easier said than done).
Anyway...I'm getting too wordy here--but I very much appreciate everyone's ideas on sound muffling and love seeing the practice spaces. I want to start making a lot more noise and need to consider muffling and room changes.