One specific part of highway 88 to be wary of is the part from Carson Spur down to Kirkwood, a mile or two before the turnoff to the resort. Often, even when the rest of the highway is dry pavement, the eastbound lane past the spur will be covered with a pretty thick layer of icy snow because it's in the shade all day.
Traffic is usually light enough that you can ride in the opposite lane. It's a good mid-winter high Sierra fix when everything else is closed.
I've noticed the west gate to Monitor Pass has a gap big enough for a bike and the snow is thinner that far east, might be worth a try.
Also, for the obscurist: Winton Road is gated at both ends starting Nov. 15th each year. That's a privately owned paved SPI forest road that can be used to connect the community of West Point with Hwy 4 near Bear Valley. A good summer shortcut to get to 4 if comng down from the north, saves you from having to run all the way down to Angels Camp and up past Murphys.
Mormon Emigrant Road and Wentworth Springs Road are also closed for the season.