You can put any sub outdoors and let it play, of course, but subwoofers which are intended for outdoor use are typically meant for live sound applications, so they are usually very powerful.
This is an example of a outdoor subwoofer, and with a powerful enough amp was shown to hit 140 dB above 50 Hz.
As far as pressurization goes, sound is just pressure waves. These waves weaken as they spread out over greater areas, but as long as you are close enough to the point of emission, you will hear them. Naturally a more powerful subwoofer will audibly affect a greater area. An advantage of bass waves is they do not weaken as much with distance as higher frequencies. This is why you can hear the 'boom' of cars with powerful audio systems a long distance away and never hear its treble.
Yes, you can use your sub outdoors, and it should still sound fine, as long as you are close enough to it. The nice thing about using your sub outdoors is you will hear the subwoofer's native frequency response. So if your sub has a flat frequency response, you will get a very nice bass sound and not have to worry about room acoustics messing everything up.
