Do minecraft mobs get harder as in game time goes by?

No, mobs don't increase in difficulty unless you have a mod that does that.

The "Regional Difficulty" (RD) will vary (& can get harder) over time, but is capped by the world difficulty level.

This difficulty level will vary from 0.75 - 6.75 & the general ranges are…

* 0.75 - 1.50 for Easy
* 1.50 - 4.00 for Normal
* 2.25 - 6.75 for Hard

There's also a "Clamped Regional Difficulty" level (which is a restricted range), that's based on regional difficulty, which effectively CRD = (RD -2) / 2. The range for this value is…

* On Easy, this will always be 0.000
* On Normal, this will vary between 0.000 & 1.000
* On Hard, this will vary between 0.125 & 1.000

This "Regional Difficulty" & "Clamped Regional Difficulty" does affect some things in the game like…

* Hunger effect when fighting Husks (7s x RD)
* Illusioner Arrow gains Blindness (when RD is 3.00 or higher)
* Chance of a Spawning Skeleton Trap Horse (1% x RD)
* Chance of burning zombies set a target on fire (30% x RD) & duration of burn (2s x RD)
* Chance zombies will break a door on Hard (10% x RD)
* Chance zombies & skeletons can pick up dropped items (55% x CRD)
* Chance zombies & skeletons will have enchanted weapons (25% x CRD)
* Chance zombies & skeletons will have enchanted armor (50% x CRD)
* Level of enchantments of weapons / armor (5 + 18 x CRD)
* Size of spawned slimes
* Chance spiders inflict a status effect on Hard (10% x CRD)

Please note that this is only noted things related to Regional Difficulty, there may be some other things that it may affect that's not noted. Regional Difficulty is based on "Player Hours" in an area as well as the current time of day (with night generating a higher RD than daytime).

Hope this sheds some light on the subject.