In Episode 2 of Sword Art Online, Kirito obtains the Coat of Midnight having obtained the Last Attack Bonus. This would be a rare item, if not unique, because it was dropped by a Floor Boss.
In Episode 3 after Sachi dies, during Christmas Kirito plans to solo the event to get the rumored resurrection item to bring Sachi back to life. While he is preparing he changes his coat to one that seems warmer.
I am wondering - can armor be customized for different climates or did Kirito get a second Coat of Midnight and if so where?
The layout of the anime is extremely non-linear, and in one episode, the whole storyline jumps 2 years into the future. This was intentional by the producers (obviously), but it does make it very hard to follow. There are always enough subtle references made by the characters in order for us to work out the timeframe of the episode.
Considering that Kirito maintains the same attire throughout the entire show, even when he joins the guild, Knights of the Blood Oath, we can see that Kirito keeps similar or the same armor/armor set. If this is the case, we can infer that he keeps upgrading Cloak of Midnight and is altering it's visuals to fit his current situation.
So the fact that it looks different on Christmas is most likely to keep him warm during this season.
Actually Kirito received 3 coats before receiving the Coat of Midnight. It was his 4th coat received after defeating the first floor boss, and yeah Coat of Midnight's also named as Blackwyrm Coat and made by Ashley. In between the 2 years gap, he may have received some coats or purchased them from virtual shops.
It is believed that The Coat of Midnight was the first coat he got, from the first floor boss, and had a couple coats afterwards (Probably the weird polka-dot one and the winter one.) before he got The Blackwyrm Coat, which is presumably another Boss Drop from a higher floor, or perhaps a player made one, we do not know which.
References, the whole first season and second season, however if it was said in some sort of developer commentary I would not know.
In some sense the coat is maybe telling that the time is now Christmas. In game aspect, maybe a limited time item with a strong buff or it is the mission requirement to get the resurrect item with that coat. Moreover just like Dasttann777 said it is not linear and the timeline is somewhat empty after the first floor until he met with Sachi.
From what I understand, he changed to the Blackwyrm coat (the one that was black) because the Coat of Midnight was too recognizable and, having announced he was a Beta tester, he marked himself as a target, and the Coat of Midnight became associated with "the Floor 1 Beater." (cheater/Beta tester). When it became a nuisance, he changed it.