As you say, the traditional celebration of the solstice was probably the main reason why December 25th was chosen as the date on which Christ's birth was celebrated. Some people argue that another contributing factor was the holiday of Dies Natalis Solis Invicti, which celebrated the birth of Sol Invictus on December 25th; however, the Emperor Aurelian instituted this holiday in 274 AD, and many others argue that he did so because Christians were already celebrating Christmas on that date.

Regarding the choice of December 25th as the Nativity, Saint Augustine said: "Hence it is that He was born on the day which is the shortest in our earthly reckoning and from which subsequent days begin to increase in length. He, therefore, who bent low and lifted us up chose the shortest day, yet the one whence light begins to increase."