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If it is able to be registered in the Snowflake breeders club, it is hom Snowflake.
If both parents are hom Snowflake, it is hom Snowflake.

If one parent is Snowflake, it is at least het Snowflake.
If it produces a Snowflake, it is at least het Snowflake.

Definitely try entering her in the breeders club, as Haltanny said. With markings like hers, that's really the only way to know for sure. These are both snowflake, but it's impossible to tell!

PFR SNF Snow Leopard


PFR SNF SBA House Cup

Also remember that even if your horse is hom for snowflake, it has to carry Lp (Appaloosa) for it to show. For instance, this poor guy, who didn't manage to get Lp from either parent. *sigh*

PFR SNF G3 Stealth Snow

But still managed to sire:
PFR G4 SNF Snufflepuff

Her sire is snowflake which means he's homozygous for it. Any of his offspring will at least be het.

@pfrsure "snufflepuff" I'm dying over here.

She's het (SNFsnf, and her sire is hom SNFSNF) The options for a foal from that pairng would be SNFSNF, SNFSNF, snfSNF, and snfSNF. So you'd only have a 50/50 chance of hom snowflake, and a 50% chance of het snowflake. Any foal is guaranteed to inherit one SNF from the sire, but could inherit her non-snowflake gene.

Two hets (SNFsnf and SNFsnf), you'd get SNFSNF, SNFsnf, snfSNF, and snfsnf. So that gives you 25% hom snowflake, 50% het snowflake, and 25% no snow flake at all. If it helps, using punnet squares can help you see your odds.