Birthdays according to calendar - confused

Sims have birthdays after so many days.

For example, on normal life span, babies age up after 3 days, toddlers after 7 etc etc.

So, when a baby ages into a toddler, their birthday on the calender is 7 days later. If you turn off aging when your toddler is 3 days old, the birthday will disappear from the calender. If you turn it back on, it will reappear where it was, so in "4 days" because 3 have passed.
So when aging is off, the Sims don't have birthdays at all.

The amount of days each lifestage is changes only when you change the lifespans from short/normal/long.

How long your seasons are don't make a difference with this but if you change it up, their birthdays may appear in a different season than they did before. THey will still be that many days away.

If your Sim passes their birthday and you don't have a party for them they will age up on their own about 24 hours after their birthday.
If you have a party for them, they age up when they interact with the cake (Blow out candles, taste icing, etc. )
There are mods that allow you to have a birthday party without aging up, otherwise I guess just invite a bunch of people over and make them give gifts to your Sim or eat cake without doing the candles, but your Sim will not think of it as a birthday party unless you use the mod, or they age up. Meaning they'll get the sad moodlet that their birthday was forgotten and then age up on their own the next day anyways.

Hope that helps.

*Note: Pregnant Sims do NOT age. So anytime a Sim is pregnant their birthday gets bumped up by 3 calendar days until the baby is born.

Lifespans
Normal:
Baby 0-3 days, usually 3.
Toddler: 7 days
Child: 13 days
Teen: 13 days
Young Adult: 24 Days
Adult: 24 Days
Elder: 10+ Days

For Short it's half of that (rounding up, so Toddler is 4, Child is 7)
For Long it's 4x that. (Toddler 28 days, Adults 96 etc)

Hope that helps.

*Note, you can always age up a Sim early, at any time. Their next birthday will then appear after however many days it should for the next lifespan age. So if you age up a toddler after one day, they will have a birthday 13 days later.

This
http://modthesims.info/d/628042/ageless-birthdays.html
The only way I know to celebrate without aging.

Aw @SimAlexandria Thanks so much for all that info, very helpful! I see I misunderstood the birthday icon completely, lol. And the seasion is random (while number of days is not random), so I will not enter every household to check the calendar, I can just as well use a dice if deciding what season my sims were born. That is actually very time consuming :) Thanks a lot! :)