One thing you can do is use the search function and add genes to the filters, see if you get many results or not!

Roughly (and excluding grade horses):

Extremely rare: Reverse Dapple (can be found in all breeds but it's an extremely rare variation of regular dapple).

Rare and exclusive: Mushroom (only exists in Shetlands and very hard to obtain), Manchado (exists in Arabians and Thoroughbreds, very hard to obtain).

Rare: Dapple (found in all breeds, seems not too uncommon but it's an hidden gene so breeding especially for it is hard), non-grey/roan percherons (roan could exclusively be obtained from Curly's stud under conditions), non-black Friesians, roan Akhal-Teke (roan could be obtained from Curly's stud under conditions + AT are a rare breed).

Somewhat rare: W# (probably wouldn't be too much trouble to pull a horse with a White gene but hunting for a specific White # when a breed has several can be troublesome).

Uncommon for breeds which naturally have these genes: Sabino/Tobiano/Roan/Overo/Leopard patterns (except for breeds like American Paints, American Saddlebreeds, Appaloose, Irish Cobs, Knabstrupper, Shetlands and maybe Welsh and Mustangs), Cream, Flaxen, Silver.

Common for breeds which naturally have these genes: Splash White (I may be wrong, could be uncommon but definitely not rare), Dun, Champagne, Pangare, Sooty.

No one cares: Rabicano, Grey (usually, unless it's a fleabitten grey).

Note: I use 'Rare' as in 'there isn't many horses with that gene/you're lucky if you pull 1 foundation with that gene for every 100-200 pulls' (unless specified otherwise). 'Uncommon' goes for 'there is quite some horses with that gene but if you're trying to pull foundations with that gene, it might take a few dozens of pulls unless you're lucky'.

Thank you so much, this was very helpful! I really appreciate it :)

I would argue now as a TB breeder that manchado has become a dime a dozen in TBs. It is more rare still in Arabians and any kind of TB/Arabian crossbreeds like Anglos, American Warmbloods, etc 

This doesn't answer what's become common through customs/breeding, but I've made a spreadsheet for the rarities of genes when pulled from the foundation store! I haven't been posting it places except when people seem to be asking a question where it'd be relevant, because I feel like my sample sizes are still unacceptably low (~100 horses for most breeds) - so take the data with a big grain of salt, because it's possible I'm just unlucky!

But it might still tell you something useful - Gene Frequencies (google sheet)

(Appaloosas, Thoroughbreds, and Arabians are the most likely to be accurate, due to them having the largest sample sizes, but y'know... there's always a chance that probability is messing with me)

Edit: oops, did not realize how old this post originally was when I saw it pop up in the "recent" box. Oh well.

Hi destinysWalrus, I just used your Gene Sheet for my wild Irish Cob, and she has the gene Sw1, which you said was 0% on Irish Cobs. Not critisising haha, just letting you know! xx

@ TabbyGirl, if you look at the sheet you'll see that Irish Cobs only have 100 foundation pulls for the data, it simply means none of the horses pulled had the Sw1 gene, not that it has a 0% chance of being pulled. Also the gene sheet is NOT for wilds, only foundation horses.

Stupid me not reading the sheet right 😭. Thank you xx