I think Jim P is correct. Last year I popped a big cow in mid-August. I had 2 igloos, a 120 and a 150. Put the bone in semi quarters, shoulders and rear, one of each in each cooler, added neck meat, rib meat, lions etc. probably 6-8 bags of ice in each. Could not lift or close either one. We threw a sleeping bag over it all for a couple hours to chill. I'd guess 1/2 or more of the ice melted in the first 45 minutes or so, tilted coolers to drain a small river of melt water. Then when cold, we boned out a quarter at a time, sacked it in a garbage bag, it all fit easily in the 150 with room for 2-3 bags of ice. I'd guess 185-200 lbs of meat.
Had I boned out the lower legs, sawed off the bone, I could have closed both coolers I think. For a big bull, if you want to leave the bone in, it'd have to be one big cooler, or have the quarters sawed to fit or bone it out. I'd guess a 250-300 quart size may work, depending on how it is dimesioned. But am not sure. I might look at soft sided coolers, Reliant fish kill bags. I've kept meat in them with ice for 2-3 days. They can leak a bit, so a pick up bed is a good idea, but you can get them in very large sizes. They have drains too.