B737-700 Captain reported during the de-icing process frozen precipitation was melting from heated cowling inlet lips and then re-freezing inside the engine inlets ahead of the compressor. Reporter stated that multiple aircraft experienced this issue and that specific guidance for this situation could not be readily found. Reporter suggested that the Aircraft Manufacturer's recommendations should be enhanced and augmented for this meteorological condition and resulting ice formation.

Narrative

While preparing to fly a flight; ZZZ-ZZZ1; we experienced rapidly changing weather conditions on the ground while operating a B737-700 (Tail # YYY). ZZZ ATIS Information Delta; Winds 020/12; Visibility 1/2 SN; Sky VV007; Temperature -22C; Dew Point -25C; Time 0253 Zulu; Altimeter 30.05; Runway XX/XXL; RCC 5. We proceeded from ZZZ Gate XXX to the ZZZ deicing area to have the aircraft deiced with both engines operating.During our time on the ground; the visibility varied between 1/4 to 1/2 to 3/4 miles. The snow intensity varied between SN to SN+. There was a period of approximately one hour with specific atmospheric conditions (1/4 SN+; temperature -22C) that multiple Company aircraft in the deicing pad were experiencing the same issue with ice accumulation in the engine intakes. ZZZ 'Iceman' reported to multiple Company aircraft Pilots that they saw ice buildup in two areas around the engine nacelle. 1. Icicles were forming under the engine nacelle.2. Ice 'blow back' was forming inside the bottom surface of the engine intake aft of the heated engine intake lip and forward of the fan blades. It seemed that each Company Crew may have handled the situation a little differently. We chose to shut down both engines while sitting at the pad. Then we requested that a heater machine come out to the pad to melt the ice from inside the engine inlet before restarting the engines. We also requested a Super tug to tow us back to a gate if the heater machine did not work. We also asked that ZZZ Operations clear a gate (with a terminating aircraft at the gate) so that a gate would be available for our return prior to the three-hour time limit imposed by the 'Tarmac Delay' program.One Crew did the same as we did; and some Crews chose to taxi back to the terminal (there were no gates available). I called Maintenance Control to confirm whether or not we could restart the engines with the ice buildup in the intake. As I suspected; Maintenance Control said do NOT restart the engines until the ice is cleared from the engine intakes. Company Ground Personnel attempted to melt the ice buildup in our number one engine (shut down) using two separate heater machines for about 15-20 minutes each.For reasons unknown; neither heater machine was able to clear the ice from our engine inlets prior to reaching the three-hour maximum time with Passengers onboard the aircraft per the 'Tarmac Delay' government rules. The ice remained in our engine inlets while the Super tug towed us back to ZZZ Gate XXY. The entire evolution from push back (XA54 local) to arrival at the gate (XF34 local) was 4 hours and 40 minutes. I respectfully request that Boeing Company conduct an engineering investigation using the parameters we had in ZZZ to confirm the problem we experienced and make 'conclusions and recommendations' on how to deal with this issue moving forward. The problem is that the snow appears to be coming in contact with the heated engine inlet surface; melting; then immediately refreezing inside the engine inlet between the heated engine intake lip and the fan blades. This situation could happen after leaving the deice pad en route to the runway; and the Crew would have no idea that the ice is accumulating in the engine intake. If that is the case; Boeing Company may be correct in issuing a bulletin which prohibits the B737 from operating in the specific weather conditions which cause this problem. I believe this is a potential Safety issue which requires further investigation by the Boeing Company.