Air carrier Captain reports no response from Dispatch after entering hold and requesting a new alternate.

Narrative

ATC issued a number of holding instructions to inbound MSP aircraft. We were holding over EAU as published on the EAU 5 Arrival. Sending an ACARS message through free text to Dispatch to inform them about our holding over EAU; present fuel on board; and expected further clearance. The First Officer and I determined 4;400 LBS for our minimum fuel for diverting to LSE if it became necessary. Our current fuel status had us being able to hold for at least 45 minutes; conservatively. During our hold ATC updated the EFC times for a number of aircraft including us. We were extended by approximately 10-15 minutes but we still had plenty of fuel on board at tht time. Shortly after the new EFC times we were given by ATC; an air carrier flight said they were going to need to divert within a few minutes. ATC said the airport had said they shut down the airport due to the weather; snow mixed with freezing rain. The MSP Airport was also in the process of swapping runways from the 12's to the 30's; but Runway 30R would be unavailable until it was cleared. The air carrier flight declared minimum fuel after a few minutes and said they had to divert and requested a heading to get themselves set up. Our fuel situation was still good at this point. Not too long after the air carrier flight diverted they were back on the frequency saying the divert airport was closed due to braking action report of 'nil.' I sent Dispatch an ACARS about coming up with a new alternate and included our current fuel status. The First Officer and I also looked up weather for various airports to use. We looked at EAU and RST. I think we might have looked into CWA as well but I'm not sure. Anyway; the weather reports we had for RST and EAU had light freezing rain; snow. We figured that both were probably in the same situation with little and/or no braking action. We looked up the weather for DLH and the report was gusty winds from the east; 4 miles visibility and snow. DLH is farther as an alternate than LSE so we came up with a new minimum fuel on our own in case our hold time was extended or could not get into MSP. During the entire hold which was nearly 45 minutes to an hour; we never received any messages or confirmations from Dispatch. After sending the first message about our holding at EAU; there was no response. When the air carrier flight returned to the frequency and said that LSE was unusable; we sent a message to Dispatch about LSE having a braking action of 'nil' and we needed a new alternate and go around possibilities of RST; EAU; and DLH -- no response. We determined on our own for DLH and our own minimum fuel because we had not heard from Dispatch. Soon after the air carrier flight returned to the frequency; they were immediately cleared into MSP and instructions for other holding aircraft soon followed; including us. We landed without incident but both the First Officer and I were more surprised that we did not hear anything from Dispatch considering we had gone down to ZZZ and had to hold as well and had all kinds of messages from Dispatch.