BE02 CREW HAD RWY INCURSION. ACR ACFT MADE A GAR.

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CONDITIONS AT CLE WERE LOW VISIBILITY AND SNOW. BRAKING ACTION WAS RPTED AS FAIR. I WAS OPERATING FLT ABCD FOR ACR X ACTING AS CAPT. RWYS 23L/5R WERE CLOSED FOR ICE AND SNOW REMOVAL. WE WERE TAXIING BEHIND A B737 ACFT Y. BOTH THE B737 AND OUR FLT WERE CLRED TO BACK TAXI RWY 23L. THE B737 WAS CLRED TO CROSS RWY 28 (AN INTERSECTING RWY) WHILE WE WERE TOLD TO HOLD SHORT. THE B737 INCREASED PWR TO CROSS RWY 28. AS A RESULT; THE SNOW THEY KICKED UP EFFECTIVELY 'WHITED' US OUT. INSTEAD OF STOPPING IMMEDIATELY AS I SHOULD HAVE; I EASED FORWARD SEARCHING FOR A PLACE TO HOLD SHORT. AS A RESULT; WE GOT TOO CLOSE TO RWY 28 CAUSING A GAR FOR AN ACFT Z ON FINAL FOR RWY 28. KEEPING THE FACTORS IN MIND ON THE REVERSE SIDE; I WOULD ATTRIBUTE THIS EVENT TO MY DECISION TO CONTINUE TAXIING IN THE MOMENTARY 'WHITE OUT.' CONTRIBUTING (BUT NOT AN EXCUSE) WERE THE UNUSUAL TAXI INSTRUCTIONS OF WHICH I HAD NEVER USED; COMPLETE ICE AND SNOW COVERAGE ON THE GND OBLITERATING ANY GND MARKINGS SUCH AS HOLD SHORT LINES OR TAXI AND RWY MARKINGS.