Hi Kaykay,
Nope, no Frame in the 100% Arenosa bloodline. The Frame pattern in American Shetlands has somewhat questionable origins. The only two patterns in the UK Shetlands are Tobiano and Splash which of course both appear in the Arenosa bloodlines. Sometime early in the history of the ASPC sabino was introduced - probably through not pure island Shetland imports. Later infusions of Hackney and Welsh into the American Shetland gene pool increased the incedence of sabino as both of those breeds have that pattern (Welsh also has Splash - sabino as far as I know is the only white pattern in the Hackney breed).
Frame only appeared in the Shetland gene pool very recently - within the last 30 years. It appeared in Iowa primarily and there has been a great deal of debate about its introduction into the breed since it is a non-native pattern. With linebreeding of those few Frame lines lethal white foals have just began appearing within the last 15 years or so.
There are part Arenosa ponies that could have Frame because of the bloodlines they have been crossed to but the Frame pattern is not present in the Arenosa bloodline.
Lewella