The Sabbath is Included
You are observing special days and months and seasons and years! (Galatians 4:10 NIV)
The NIV Study Bible gives this note of explanation for their translation:
4:10 special days. Such as the Sabbath and the Day of Atonement (tenth day of Tishri; see Lev. 16:29-34), which had never been, and can never be, in themselves means of salvation or sanctification. months and seasons. Such as New Moons (see Nu. 28:11-15; Isa. 1:13-14), Passover (Ex.12:18) and Firstfruits (Lev, 23:10). years. Such as the sabbath year (see Lev. 25:4). The Pharisees meticulously observed all these in an attempt to gain merit before God.
However, "special" is an interpretation. The text is simply "days:"
days ye observe, and months, and times, and years! (Galatians 4:10 YLT)
ἡμέρας παρατηρεῖσθε καὶ μῆνας καὶ καιροὺς καὶ ἐνιαυτούς
Clearly Paul is referring to things detailed in the Old Testament. The "appointed" times are the weekly Sabbath, the Passover, the Feast of Unleavened Bread; the Feast of Firstfruits; the Feast of Weeks; the Feast of Trumpets; the Day of Atonement, and the Feast of Booths (cf. Leviticus 23).
While Paul does not specify which days, it is highly unlikely those he addressed would be observing "days" like the Passover which only occurred once a year and not be observing the weekly Sabbath.
The Cambridge Bible Commentary explains this passage depends on the meaning attached to παρατηρεῖσθε which is translated "observe:"
The whole meaning of the verse depends on the sense attached to this word. It is compounded of a verb which means to observe and a preposition which implies that either the purpose or the method of observation is bad. The simple verb and corresponding noun are commonly used in N. T. in a good sense, e.g. “He that hath my commandments and keepeth them, he it is that loveth me”. John 14:21, ‘Circumcision is nothing, and uncircumcision is nothing; but the keeping of the commandments of God.” 1 Corinthians 7:19. But the compound is never so used. Mark 3:2; Luke 6:7; Luke 16:1; Luke 20:20; Acts 9:24. Comp. for the noun, Luke 17:20. St Paul is not condemning the observance of ‘days and months and times and years’ but their mis-observance. Jewish Christians might continue to keep them as hallowed customs of divine origin, but not as grounds of justification. These were not to be sharers with Christ in the great work of salvation. Bondage to these rudiments forfeited the liberty of the Gospel. Gentile believers were never bound to such observances, and if they yielded to the Judaizing teachers and submitted to the yoke of the Jewish ceremonial, they were no longer partakers of the liberty of Christ.
Compare Colossians 2:16, where not the simple observance is condemned, but the slavery which is involved in its being required for salvation, and the dishonour which is done to Christ by adding to His perfect righteousness. See note on ch. Galatians 5:2.
days] ‘sabbaths and fasts’. There is clearly no exemption here from the obligation of the observance of ‘the seventh day’. ‘The law of the Sabbath, i.e. of one weekly day of holy rest in God (the seventh in the Jewish, the first in the Christian Church) is as old as the Creation, it is founded on the moral and physical constitution of man, it was instituted in Paradise, incorporated in the Decalogue on Mount Sinai, put on a new foundation by the Resurrection of Christ, and is an absolute necessity for public worship and the welfare of man’. Dr Schaff. What St Paul condemns is the observance of the day in a legal spirit, in compliance with the minute and childish prohibitions of the Rabbinic system and as a matter of merit with God.
"Observe" must be considered in context:
Formerly, when you did not know God, you were enslaved to those that by nature are not gods. But now that you have come to know God, or rather to be known by God, how can you turn back again to the weak and worthless elementary principles of the world, whose slaves you want to be once more? (Galatians 4:8-9 ESV)
As Gentiles, before receiving the Gospel, the Galatians had not been observing any of the "days" required in the Old Testament. Therefore, Paul's statement cannot mean the Galatians had turned back to observing them. Rather, as the Cambridge Commentary states, what Paul is concerned with is "the mis-observance." The situation is similar to that of the Gospel where Jesus observes the Sabbath and yet the Pharisees continually accuse Him of doing so improperly. Jesus did not acquiesce to the Pharisees, but He continued to observe the Sabbath.
After receiving the Gospel, Paul taught the Gentiles how God expects His people to live. The emphasis was to understand the Law because God had saved them, not as something which brought salvation. Notice, what Paul says next: "Brothers, I entreat you, become as I am..." (v. 11). Paul observed "the days;" in particular he would be found in the synagogue on the Sabbath.
It is clear that Christians preserved the practice of meeting every week. Acts states they gathered weekly to break bread (Acts 20:7). Pliny the Younger records they gathered weekly to sing a hymn to Christ as to a God and then shared a meal. Where the Pharisees focused on what constituted legal observation, the Christian emphasis was on meeting for fellowship and worship.
1. NIV Study Bible, Fully Revised, Revision Editors Kenneth L. Barker, John H. Stek, Walter W. Wessel, Ronald Youngblood, Zondervan, 2002, p. 2423