I've never travelled on a Snowflake ticket myself, but they are very similar to an ordinary SK ticket... (Well, they are often more expensive even, so...)
No difference in any EBG benefits, and you will have the same online checkin possibilities (with exactly the same seats to choose from as regular Economy).
Regarding the bagage, the official line is that there is no interlining of bagage to/from snowflake flights. But I do think that it is still possible... Nowadays airlines seem much stricter on whether they allow throughcheck of bagage on separate tickets etc though. But between bmi and SK with a comfortable connection time, and as you're EBG I wouldn't be too worried, really! I don't know how the e-ticket confirmations look now with the new PDF system in place, but prior to that I know that they were identical to regular e-ticket confirmations in C/Y/M, so no way for the check-in agent to see that it is a snowflake ticket (except for fare basis). You can even printout a travel plan from regular SK website on a snowflake booking.

Is this from UK to Scandinavia? Remember that the regular SK return tickets are very nicely priced (mostly £89-99), bmi are now offering cheap tickets on their codeshares (since mid April) and BA has started one-ways on cheap tickets. So there are plenty of alternatives... But I think that you will have the same chances of through check with snowflake and regular SK economy. (Just forget to mention that it is snowflake)