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She will only show snowflake if she is homozygous for the snowflake gene. See if she can be entered in the Snowflake breeders club, if she can then she is definitely homozygous for snowflake. Heterozygous won't show so you will need to breed her to other snowflake horses to find out. If she is carrying snowflake then breeding her to a homozygous stallion will give you a 50% chance of getting a homozygous foal, with 50% of a heterozygous. Breeding her to a heterozygous stallion gives you a 25% chance of homozygous, 50% chance of a heterozygous and 25% chance of no snowflake at all.
Any foal would need have at least one copy of appaloosa to express snowflake.

It is the appy genes that are causing those spots; appy horses varnish and that results in some spotting. Together with the w8 spotting that can be very confusing! As White Valley said, snowflake only shows when it is homozygous and she can be entered in the breeding club. If you look at her parents / ancestors there are no snowflakes in the lines, so that's another way of knowing she cannot be snowflake.

In this buddychat (in the description )there are some images of appy varnishing over time: https://www.huntandjump.com/buddy_chat.php?chatid=644
You can see they get all 'spotty' first, and eventually all appys turn white if they're old enough