3-13 years. Seriously! I have seen kids in middle school who still refuse to blow their nose, they prefer to sniff it up instead, driving their parents crazy! but, many children, around age 3-4, can be taught how to use a tissue to blow their nose........Before that, it's up to mom or dad to chase them around with the tissue!
2 years. Children can learn to blow their noses if the parents playfully start teaching the children from about 18 months onward. Some kids don't like to blow their noses, and won't do it even at age 5-6 years.
2 years. Blowing your nose is a learned behavior, so takes time and practice. But even toddlers can play these games: start by blowing through the mouth - bubbles, or blowing pieces of paper across the floor (have a race). Then practice doing that using the nose. Then "blow the hankie" using a tissue. You can teach your child to blow their nose. Dr. Hana solomon describes this in a great article.
Any. Each child has their own time table for this ability. It's not so easy a skill to teach. I have had some success with getting a child to "blow" out birthday candles as hard as she can, using a tissue instead of candles, and then repeating the process while she closes her mouth so she feels the air come through her nose. Some just get the idea early on and do it. Almost all kids can by 2-3 yrs.