Is it common to have breathing difficulties and feeling of pressure on throat after SMAS facelift?

It is very unusual to have a complication like this a year out. I would meet with your surgeon just to have your neck examined. I wish you the best!

It is unusual to have these sort of symptoms a year after surgery. You are best to have this checked out.

You would need to ask your surgeon what he did in your neck. Some surgeons do a plastysmaplasty for banding using sutures, others may use threads across the neck.  It is often these threads or sutures that can tether and cause this sensation. 

 Hi, I have performed many SMAS facelifts and neck lifts for over 30 years and have performed many minimally, invasive SMAS facelifts.  The reality is that there are many different ways to perform a facelift from incision length, incision placement, level of tissue dissection (skin only, SMAS, Deep Plane, Subperiosteal), different degrees of tissue undermining, how to lift and support (imbrication versus plication of the SMAS layer), how much excess skin to trim, is excess fat going to be reduced and finally will the overall shape of the face be made more feminine or masculine (while avoiding the over pulled, windswept appearance).  This would include various methods of tightening the platysma muscle in the neck.  A typical SMAS face and neck lift should produce that sensation a year post-op.
 Typically the muscle is plicated (folded upon itself) using multiple permanent sutures in a straight vertical line down the middle of the neck through a small curved incision under the chin.  There is an older suspension technique, I see sometimes used, that attaches from the bone behind one ear all the way across the neck to the other side.  This has been know to create the type of discomfort you describe and the phrase "clothesline effect" has been used to describe it associated with this technique.  For that reason I don't use this technique but I've had patients with this done elsewhere come for revision face and neck lifts and have found and removed the suspension suture causing the issue.
 Your facelift Surgeon is the only one who knows for sure what was done and what might be causing the symptom(s) that you describe.  You might want to have that conversation with your facelift surgeon.  If that was used, the large permanent suture can be found and cut which eliminates that pressure on the larynx (wind pipe).
 Hope this helps.