The solstices and equinoxes changed recently (1488 DR)
At the end of the Second Sundering, the traditional days of season changing shifted. The Sword Coast Adventurer's Guide has the details (pg. 15):
The worlds of Abeir and Toril drifted apart in 1487 and 1488 DR. In some places this change was accompanied by cataclysm, while in others the shift went ...
You can find detailed information about the calendar of Harptos on the FR wiki, which even has a nice picture depicting when the seasons used to start for all the past editions of D&D:
Winter Solstice (Nightal 20) is the beginning of winter.
Spring Equinox (Ches 19) is the beginning of spring.
Summer Solstice (Kythorn 20) is the beginning of summer.
When the text is unclear, look for examples
Surprisingly this relies more on text interpretation than rule interpretation, which is probably where the confusion lies.
Normally a weapon description would list a die number (1d6, 2d6, 1d4, etc.) in a table for the damage numbers. From there it was on the player to know to add your ability modifier based on ...
It's unclear from the text
Normally you'd use your Dexterity for the attack, but normally the damage roll uses the same modifier as the attack roll (implying that you should use Strength for the attack). It's not clear which of these rules should override the other one.
When the rules are unclear, we on StackExchange can't and shouldn't issue rulings for ...
You use your Strength modifier for the attack roll and the damage roll
The section in the PHB on Damage Rolls states (emphasis mine):
When attacking with a weapon you add your ability modifier - the same modifier used for the attack roll - to the damage.
So the general rule is that the damage roll uses the same ability modifier as the attack roll.
You add your Dexterity to the attack roll, because the weapon doesn't say otherwise so the rules on Ranged Attacks still hold.
For the damage roll, however, it seems like you are supposed to add both Strength and Dexterity for the damage roll. Reading the item's unique features, you get to add your STR to the damage as an additional modifier, and then you ...
Specific trumps general
The general rule for Dexterity-based attacks is that you add your Dexterity modifier to the damage if you hit. The rules for weapons list the basic damage for each, and you add your Strength or Dexterity bonus when applicable.
That specific longbow, however, states that the damage it does is 2d6 + the wielder's Strength modifier. ...
I'm going to post a contrary opinion here. I'm going through this right now with my table, and what hasn't been mentioned here is this bit (emphasis mine):
Characters who place the security of the city and the realm ahead of
their own interests are invited to join this faction. Potential
recruits must be residents of Waterdeep.
The second sentence ...