Jenny,
my "studio" consists of the two Alien Bee 400s I bought in 2000, two light stands, a backdrop stand and a variety of backdrops. I can set that up anywhere either in my own home or in the home of a client. The portability factor was very important for me since I bring this setup to the dog shows I shoot. But I've used it as well for pet portraits and the fact that you can bring it with you makes it more convenient for the animals I shoot since they can stay home and be comfortable.

I use the strobes for outdoor shoots as well when I want to be absolutely sure of the lighting and control the shadows. Yes, I've had that setup in a home studio and it was convenient but you don't always have to have a physical studio to take studio portraits. And learning how to use studio strobes greatly increases your versatility and what you can offer professionally.

Jim