I-80 from SLC to Cheyenne will be different for sure than I-70 through Colorado.
Wind is always a factor in Wyoming; however, in April, it is frequently a tail wind that you'll have when travelling eastbound, as storms will usually (but not always) be coming out of the northwest.
Storms to worry about are the ones that come out of Arizona/New Mexico and move across Colorado and set up in northeast Colorado. These can be goodly snow producers for southern Wyoming. And March and April are snow months in Wyoming as well as in Colorado.
Keep an eye on the weather and be ready and willing to hunker down somewhere for a day or so. Ground blizzards are not uncommon along I-80 with the combo of snow and wind, with stretches of the interstate shut down for a while.
The high point on I-80 is just east of Laramie WY. Something of a climb out of Laramie (at ~7200ft) to about 9600 feet, then it levels off and is pretty much downhill all the way east from there. Rolling hills between Laramie and Cheyenne, then flattens out a bit more from Cheyenne to Pine Bluff and on in to Nebraska.
