I knew I didn't want people coming to my home--not so much the fear of strangers as what they would think of my housekeeping skills! Now I'm getting more comfortable with the idea, and I actually have a space in mind to use, but nothing has been done about it yet.
When I decided to start reading for others, I called a couple of metaphysical shops in the area and asked if they had reading rooms available and whether they would charge a flat room rental fee, or a percentage of my take from the readings, and within the first two phone calls I found a place that has worked out very well. I've been there for four and a half years. I have heard of readers going into beauty shops or coffee shops and finding space there to read, as well.
I don't advertise and never have. I'm sure it works well for others, but I get all my business from walk ins and referrals.
If you are having strangers come to your home, I would advise that you tell them when they are making the appointment something like, "I hope you don't mind that my husband/roommate/brother/gigantic dog will be there. They won't bother us during the reading," or something like that, to let them know you won't be all alone. If you can actually arrange for that person or critter to be there, all the better.
Also, make sure someone knows the name and contact information of the person you will be reading for. And if you get a hinky feeling while talking to this person on the phone, tell them you aren't doing readings right now, but you can get back to them if you should start up again.
I got the above information from a couple of massage therapists, a psychic, and my Hakomi therapist, all of whom are women who have people come to their homes all the time and have never had a problem. But they all emphasized heeding their intuition, and all of them have turned away potential customers if they don't feel right during the initial phone call, even if they couldn't put their finger on what didn't feel right.
Can I just ask what you mean by cold readings, though? When I've heard that term used about certain readers, it was not in a complimentary way, as they meant someone who does not really know the cards, but gains information on the sitter by conversational or body language cues. In your case, I thought you meant reading for people you don't know. Is that right?