Old Concrete Board with horse hair w/asbestos
What you should know is that asbestos was used in plaster up into the early 1980s, particularly in textured finishes like popcorn ceilings. It was also used in drywall and drywall compounds by some manufacturers as well as sheet flooring, insulation, vinyl tile, caulking, wire jacketing and on and on. It's use in old plaster like horsehair largely depended on how available it was in the local area. Now, if it does contain asbestos and you go tearing the stuff out keep in mind that you will release microscopic fibres into the inside of your home that will stay airborne for weeks, or even months. That is the same air that you and your family will be breathing. If you are concerned about it, send a sample to a lab that has the capability to test using the PEL method. They will return a report with the percentage quantity of big A and the type. Anything over 1% is considered asbestos containing material (ACM). New York was one of the first states in the country to regulate asbestos abatement and has some really picky laws about removal and disposal. If you want to do it yourself, at least use a half face respirator with P100 filter cartridges, an exhaust fan and wipe everthing up with a damp cloth, including yourself before you leave the room. I'd guess that you don't have the big A, but then I've seen it show up in some really wierd places. Sad thing is it can take up to 20 years to snag you and by then you'll have forgotten about this renovation project. Only you can decide how comfortable you are with ripping and not knowing.