Quick and to the point, I'm aware that if you make an attack (which a grapple is) against an opponent you are hidden from you gain advantage, but since a grapple also is a contest roll, does the opponent also roll at disadvantage?

Unless a DM determines otherwise, you do not get advantage and the opponent does not get disadvantage

The rule for Unseen Attackers states:

When a creature can’t see you, you have advantage on Attack rolls against it.

The rules for Grappling state:

Using at least one free hand, you try to seize the target by making a grapple check instead of an Attack roll

What this means is that, by making a grapple attempt instead of a melee attack, you do not get advantage nor does your opponent have disadvantage because the rules for Unseen Attackers does not convey any sort of penalty to a creature making ability checks against unseen attackers.

That said, as Linksassin points out a DM is always free to use the general rule for disadvantage/advantage to impart one or both of these to the grapple participants:

The GM can also decide that circumstances influence a roll in one direction or the other and grant advantage or impose disadvantage as a result.

No.

If you are hidden from your target when you attack it using the Attack action, you indeed have advantage on an attack roll (see Unseen Attackers and Targets):

When a creature can't see you, you have advantage on attack rolls against it.

And a grapple is indeed a special attack made using the Attack action (see Grappling):

When you want to grab a creature or wrestle with it, you can use the Attack action to make a special melee attack, a grapple.

However, grappling doesn't actually involve an attack roll (same section as above):

...you try to seize the target by making a grapple check instead of an attack roll: a Strength (Athletics) check contested by the target's Strength (Athletics) or Dexterity (Acrobatics) check (the target chooses the ability to use).

Since it's not an attack roll, you don't have advantage on it due to being hidden.

Furthermore, there's nothing in the rules to suggest that being hidden applies advantage or disadvantage to any ability check. The fact that an attack roll made from hiding normally has advantage does not imply that an ability check made from hiding would be made with advantage, nor that it would confer disadvantage on the ability check made by an opponent in a contest.

In addition, there is no general rule that if you have advantage in some scenario then your opponent automatically has disadvantage in the reverse scenario. For example, there's no rule to suggest that if you have advantage on an ability check then your opponent has disadvantage. There are some specific rules that work in this way (for example, if you are invisible and your opponent is not then your attacks are at advantage and theirs are at disadvantage), but in such cases the dichotomy is explicitly stated in the rules.

There's no rule that says you do

Rykara and Bloodcinder's excellent answers do a good job of explaining that there is no explicit rule that grant advantage or imposes disadvantage when the grappler is unseen.

When a creature can't see you, you have advantage on attack rolls against it.

You gain advantage on attack rolls, that's it. However...

Your DM may rule you do

From the general rules on advantage/disadvantage we have the following:

The GM can also decide that circumstances influence a roll in one direction or the other and grant advantage or impose disadvantage as a result.

This is a final catch-all, DM-knows-best rule that is designed for situations like this where the rules don't quite cover it. Your DM may choose to rule that you have advantage on your check, or the target has disadvantage. I wouldn't suggest applying both as this would be too strong.

At my table I rule that the target has disadvantage on their check as they were unprepared for it. This only applies to the initial grapple attempt however and attempts to break free are made as normal. This has never caused an issue (not that it has come up that often) and makes the players feel rewarded for intelligent play.