Nose Object Problems If one practices Goenka style  Vipassana or Anapana meditation then the main object of contemplation is the nose area. 

If one has a cold and the nose is blocked then is it o.k. to breath through the mouth, chest or abdomen(in the Goenka, Anapana or any Buddhist meditation that uses the nose area)?

If, in that situation, it is proper to breath through the mouth,  then are there any special instructions for breathing through  the mouth in Anapana, Goenka or any other Buddhist meditation practice that uses the nose area?

What if one has always found it difficult to breath through the nose because of a partial blockage or some unknown condition that might be psychological?
If breathing is difficult concentrate on the sensation at the focal point. Apply (Vitarka) Sustained (Vicara) Attention Directing your Mind (Manasikara) to keep your mind on the focal point to cut out Thinking and Pondering / Verbal Fabrication (Vachi Sankhāra). Even with a stuffed nose you still breath hence you can just concentrate in the in and out flow. I don't think it is very advisable to breath through the mouth through.

See my answer: https://buddhism.stackexchange.com/a/12342/295 which contains more  details.