The short answer is that yes, you can cut roof rafters to include stairs for your attic. You can make the stairs as wide as you need them to be, and you can make your rafters out of any type of material. However, there are a variety of building codes that must be adhered to on a federal, state and local level, and part of your responsibility is building the house to code. Otherwise, your house could be condemned.
There is much more to cutting roof rafters for an attic stairwell than merely cutting the wood. Rafters are a load bearing part of the house, which means the weight of the roof rests on top of the rafters. If this weight isn’t accounted for in the proper manner, the roof can cave in, bringing the house down. There are specific requirements for bracing as well as rafter thickness when you start cutting into rafters, and you have to follow these rules for safety.
If you are trying to cut the rafters after the fact, when the house is already built, you have a far more challenging task ahead of you than if you had cut the rafters during the initial construction. Once the roof begins to carry the weight of the overall roof structure, it becomes dangerous and difficult to modify the structure. A simple cut can weaken the overall roof, and there are numerous bracing steps that have to be taken, starting with rafter post jacks to hold the roof up while you cut out your stairwell space. You also need to determine how to brace the rafters after the fact.
Never, under any circumstances, attempt to modify the rafters of a home without the specific guidance and planning of a structural engineer. This goes for cutting the rafters before the house is built and also after it is already in place, but it is even more crucial that you work with the guidance of a licensed professional if you are modifying an already existing structure. Failure to do so can result in serious injury. Cutting roof rafters is not something the average do-it-yourselfer should attempt to do on his own.