The Bible actually does have a couple verses that covers this situation. Romans 14:5,6 "One man esteemeth one day above another: another esteemeth every day alike. Let every man be fully persuaded in his own mind. He that regardeth the day, regardeth it unto the Lord; and he that regardeth not the day, to the Lord he doth not regard it." Paul repeats the same idea in Colossians 2:16,17 "Let no man therefore judge you in meat, or in drink, or in respect of a holy day, or of the new moon, or of the sabbath days: Which are a shadow of things to come; but the body is of Christ."
What Paul is saying is that there is no specific law about what days should be worshiped or what holidays should be kept. If you read the New Testament there is not a single commandment anywhere to keep any holidays (including Sunday services.) The requirement to keep special feast days or worship on a certain day of the week was part of the Mosaic Law, and is not carried over to Christianity.
Rather Paul is saying that if a person is convinced that they should keep a holiday as a worship to Christ, then for them it is the right thing, and no other Christian should judge them. They are showing respect and love for God. and celebrating what he did for them. That is never wrong.
However, if a person chooses not to celebrate that day, or does it in a different way, then that is also correct because they are showing their respect and love for God. And no other Christian should judge them.
The keeping of "Easter" can be found in the writing of the early church fathers as far back as the late first century (with 30-40 years of the time Paul completed his writings.) The celebration of the Paschal (as it was called at the time) was done during the same week as the Passover. There was debate on where Christians should celebrate by taking the Passover feast (as it was a Passover feast that was the "Last Supper", and Jesus told them "keep that" until he returned) the evening before, then celebrate the Death of Christ the next day, or whether they should wait and take Communion (the sacrament that comes out of the last Passover meal) and the Sunday of his resurrection. Because the day of the Passover changes each year, it was easier for the church to celebrate the Resurrection on Sundays since they were already meeting then. So by the late second century that was the common practice.
Christmas was actually celebrated by the early churches in mid-January rather then December 25. It is still practiced on that day in many Orthodox churches. As the actual day of Christ's birth is not known, it was decided within the Roman part of the church to celebrate on December 25 (the date of the largest pagan feast in the Roman world) to give the Christians an alternative to celebrate on that day. Kind of like the thousands of churches in the US today that offer "Harvest Celebration" and similar alternative to Halloween parties on October 31. It gives those who do not want to celebrate the pagan holiday an alternative. As there are no instructions saying to celebrate Christmas, nor how to do it, then the giving of presents at that time is just as valid a way to celebrate as any other.
So the rule is simple when it comes to holy days in the Christian faith. Do what honors Christ for you, and everyone else keep their mouth shut, and honor Christ they way they way instead.