These are

Winter Bash 2016 hats!

The first two models were complete opposites.

Abominable is for closing or deleting, No Longer Grinchy is for reopening or undeleting.

In the second pair, one of the models was almost forty times as big as the other one.

925 / 24 = 38.5 (nearly 40)

Of the next pair, one emitted sound, and the other one light and warmth.

Amped Up is a boombox, Fiery references fire. (This could also be Bûche de Noël, a log fire, but this is used in another pair)

The fourth pair were a light and a dark one.

I Am Your Father is Darth Vader, Search You Must is Yoda - figureheads of the darks and light side of the force respectively.

The next ones were almost twins, the host said something about one being twelve days older than the other.

Epiphany (January 6th) is 12 days after Bûche de Noël (25th December).

Pair number six were known for winning gold and bronze medals, respectively.

A gold medal is for first place, so First Responder, and bronze is for third place, so Third Time's A Charm

The final ones had appropriate names for the objects they were presenting.

All the hats have names related to how to get them, so these could be anything...

These are

Winter Bash 2016 hats!

The first two models were complete opposites.

Abominable is for closing or deleting, No Longer Grinchy is for reopening or undeleting.

In the second pair, one of the models was almost forty times as big as the other one.

925 / 24 = 38.5 (nearly 40)

Of the next pair, one emitted sound, and the other one light and warmth.

Amped Up is a boombox, Fiery references fire. (This could also be Bûche de Noël, a log fire, but this is used in another pair)

The fourth pair were a light and a dark one.

I Am Your Father is Darth Vader, Search You Must is Yoda - figureheads of the darks and light side of the force respectively.

The next ones were almost twins, the host said something about one being twelve days older than the other.

Epiphany (January 6th) is 12 days after Bûche de Noël (25th December).

Pair number six were known for winning gold and bronze medals, respectively.

A gold medal is for first place, so First Responder, and bronze is for third place, so Third Time's A Charm

The final ones had appropriate names for the objects they were presenting.

Shapchat and Just Here For The Hat contain the word "Hat" in their names.

These are

Winter Bash 2016 hats!

The first two models were complete opposites.

Abominable is for closing or deleting, No Longer Grinchy is for reopening or undeleting.

In the second pair, one of the models was almost forty times as big as the other one.

925 / 24 = 38.5 (nearly 40)

Of the next pair, one emitted sound, and the other one light and warmth.

Amped Up is a boombox, Fiery references fire. (This could also be Bûche de Noël, a log fire, but this is used in another pair)

The fourth pair were a light and a dark one.

I Am Your Father is Darth Vader, Search You Must is Yoda - figureheads of the darks and light side of the force respectively.

The next ones were almost twins, the host said something about one being twelve days older than the other.

Epiphany (January 6th) is 12 days after Bûche de Noël (25th December).

Pair number six were known for winning gold and bronze medals, respectively.

24 is for getting a gold badge, not sure about bronze yet

The final ones had appropriate names for the objects they were presenting.

All the hats have names related to how to get them, so these could be anything...

These are

Winter Bash 2016 hats!

The first two models were complete opposites.

Abominable is for closing or deleting, No Longer Grinchy is for reopening or undeleting.

In the second pair, one of the models was almost forty times as big as the other one.

925 / 24 = 38.5 (nearly 40)

Of the next pair, one emitted sound, and the other one light and warmth.

Amped Up is a boombox, Fiery references fire. (This could also be Bûche de Noël, a log fire, but this is used in another pair)

The fourth pair were a light and a dark one.

I Am Your Father is Darth Vader, Search You Must is Yoda - figureheads of the darks and light side of the force respectively.

The next ones were almost twins, the host said something about one being twelve days older than the other.

Epiphany (January 6th) is 12 days after Bûche de Noël (25th December).

Pair number six were known for winning gold and bronze medals, respectively.

A gold medal is for first place, so First Responder, and bronze is for third place, so Third Time's A Charm

The final ones had appropriate names for the objects they were presenting.

All the hats have names related to how to get them, so these could be anything...