Going to Umrah once in a lifetime is a practice (sunnat al-muakkad) of our Prophet (p.b.u.h.). Performing Umrah is wrong (makruh, nearly forbidden) on the eve of and during the four days of Eid Al-Adha. It can be performed on any other day.
The months of Shawwal, Dhu al-Qa’da and the first ten days of Dhu al-Hijja are the season for the Pilgrimage (Hajj). Hajj would not be obligatory to a person who performed Umrah out of Hajj season, just because he/she has seen the Ka’aba.
Whoever performs the Umrah within the Hajj season may wait for the tenth of Dhu al-Hijja there. That means, he/she has had the opportunity to perform Hajj. The Muslims who do not perform Hajj although they had this opportunity, would be responsible for this.
People coming to Mecca al-Mukarramah from distant locations for Umrah should perform Umrah out of Hajj season, unless they performed Hajj before. If they arrive at Mecca within the Hajj season, then they should wait for the days of Hajj and fulfill their duty of Hajj, too.