CalTrans is pretty good about keeping the roads clear unless it's a massive storm. If the advance weather forecast for the week you plan to travel shows chance of snow or freezing temps, I wouldn't take the MH. If the weather looks OK then you shouldn't have a problem unless a freak storm pops up (not very likely). The forecasters are usually right on for the I-80 corridor over the Sierras.
Here's an example... I had two of my employees in separate vehicles heading up to Reno for some work. A storm was forecast for late in the day. One decided to go up 395, he got through before the storm hit. The other decided to go across I-80 from I-5, he had to wait out the storm in Auburn until the next day. The guy using 395 had paid attention to the forecast and calculated he could make it before the storm hit the eastern side of the mountains.