I have been told that the only thing I am able to take for a cold is paracetomol, because aspirin and ibuprofen can affect you INR.
Before you buy anything get the pharmasist to look it up to make sure it wont interact.
In general do not take any medication, including "cold medicine" that contains aspirin, may do. This is the case for aspirin in any form, when on an anticoagulant.
There are many cold/allergy medicines that are aspirin-free.
You should always check with your doctor. Antihistamines should be ok, but any drug addition to your current regeime can change metabolism and require closer monitoring of the coumadin (INR) levels