So, another wiki contributor made a comment on one of the pages about an experiment they were planning with cows. I decided to take inspiration and test out sheep and chickens as well, on a much smaller scale.

My first result is in and it confirms something important: the amount of care you give an animal does affect when it will start producing better products. This suggests there is indeed a hidden statistic for each of your animals which is based on the amount of care you've given it. It also disproves the year theory which I've seen floating around (1 year from 1 produce tier to the next).

Here are my results so far:

On Winter 1, Year 4, I placed 2 chickens, 2 sheep and 1 cow. One of each species receives full care. The other sheep and chicken receive only food (apart from egg harvesting/shearing). There's no full care cow because the other wiki contributor will do a better cow experiment.

Full care chicken: placed Winter 1 Y4; medium egg Spring 17 Y5; large Winter 2 Y5; gold Fall 2 Y6

No care chicken: placed Winter 1 Y4; still producing small eggs as of Fall 2 Y6

Full care sheep: placed Winter 1 Y4; medium wool Spring 14 Y5; large Winter 2 Y5; gold Summer 4 Y6

No care sheep: placed Winter 1 Y4; still producing small wool as of Fall 2 Y6

Full care cow: placed Winter 1 Y4; medium milk Spring 12-14?? Y5, large milk Winter 1 Y5; gold milk Summer 1 Y6

Note: Unfortunately, after 1 and a half in-game months I was basically sleepwalking through the routine of caring for them and didn't notice exactly when the cow started producing medium milk. Also, as sheep can only be sheared every 3 days, it may have reached medium wool level at any point in the 3 days after its last small wool shearing. So it's difficult to pin down the exact timing of both, but as I now suspect cows and sheep both level up at the same time if given the same amount of care, the other wiki contributor's experiment may be able to give a more precise timing, provided they are more attentive than me ;)

So, in any case, it seems like it takes somewhere between 30-34 days for sheep and cows to go from small to medium if they are given full care every day. I'll continue the experiment to get more results, then post 'em here.

Edit: full care chicken gave its first medium egg on Spring 17, which suggests ~37 days for a chicken to go from small to medium with full daily care.

2nd Edit: Full care cow finally reached large milk on Winter 1, Y5, exactly one year after I put it in my barn. This means it took at least 45 days to get from medium to large. I expect the full care sheep will give large wool on Winter 2 (its next shearing)

3rd Edit: Full care chicken and full care sheep both reached large on Winter 2 Y5. (Actually, the full care sheep gave medium, but the 4 other sheep I placed on Winter 1 Y5 gave large - I think I just forgot to brush the full care sheep a couple of times - it's at the end of a row of cows so I must have switched to the milk pump before remembering to brush it)

4th edit: All my cows reached gold milk on Summer 1 Year 6, at least a month earlier than I expected (which is a little odd!). As the experiment started on Winter 1 Y4, this means it took precisely one year and a half, or 120 days. But the chicken and sheep are still on large. I guess they will upgrade soon too.

5th edit: full care sheep got gold on Summer 4 Y6, full care chicken is still holding out on me. 

6th edit: full care chicken finally got there on Fall 2 Y6. Weirdly long time.

Anyway, that marks the conclusion of the experiment. I've given hope on those no care animals. So here are my results:

Full care chicken: S to M 37 days, M to L 44 days, L to G 60 days ... TOTAL S to G: ~141 days

Full care cow: S to M 30-36 days, M to L 40-44 days, L to G 40 days ... TOTAL S to G: 120 days

Full care sheep: S to M 33 days, M to L 48 days, L to G 42 days ... TOTAL S to G: 123 days

Conclusions:

1. Chickens seem to take the longest overall to reach gold level. Cows and sheep are roughly on par. Sheep took a few days longer than cows, but this might be attributable to the fact you can only shear sheep every 3 days, making it impossible to observe their produce level in the intervening period. There is also some likely human error where I may have forgotten to fully care for the sheep on a small number of days.

2. Giving extra care (picking up/brushing/talking) to animals is the only way to upgrade their produce. This seems to be linked to some hidden statistic, which for simplicity's sake we will call "affection". Feeding and milking/shearing does not raise affection.

3. However, extra care seems to have no other benefit apart from raising affection. Therefore, it is entirely optional. If you want/need to, you can neglect to brush/talk to/pick up your animals. Their affection will not drop, they will remain happy, and they will continue giving produce as long as they are fed every day. In particular, there is virtually no benefit to continuing to give your animals extra care once they reach gold tier (apart from to help protect against product downgrading, as mentioned in the next point)

4. Feeding is essential. If you do not feed your animals, they will suffer a drop in affection each time they are not fed, possibly causing their produce to downgrade. (After gold tier you can protect against this by continuing to brush/talk to/pick up your animals for a while after they reach gold, to build up an affection "buffer zone".) They also will not give produce the day after not being fed. If you continue to starve your animals, they will die.

That's about it. I'll get to work on updating the Raising Animals page :)