I train differently outside the dojo than I do when I'm there.
At the dojo I have the advantage of controlled conditions such as a flat floor, air conditioning, lots of open space, loose fitting clothing, no shoes, and a variety of willing training partners.
It's important to practice karate in various places and ways in order to approximate different conditions that might occur in a realistic self-defense situation.
When I practice on my own, I try to practice in a variety of footwear and clothing, at various times of day, on various terrain, etc, in order to approximate a more realistic environment and to introduce challenges to movement.
In general, I don't have much room at my house to practice. It's actually surprising how little room you need to practice karate. I've found that I can do most of the kata within a 3'x5' space. It takes modification of the stances and special footwork, but it can be done.
When I want some variety, I'll put on my hiking shoes and head to the woods behind my house. This is a good environment to practice in because of the uneven ground and the proximity of trees, roots and other obstacles.
Since I live in Florida, I wear flip flops and shorts for about 75% of the year when I'm not at work, so I also practice in these clothes to gain realism in my training. When I occasionally get to the beach, I like to train on the sand and in the surf either early in the morning or late at night when no one is there to watch.