Route to Oregon

#1
We are full-timers in a 2007 Cougar fifth-wheel towed by a '03 F250. We are currently in Naples, FL but want to move across the country to Portland, Oregon region at end of December/January (we will be leaving from western edge of Arkansas after family visit).

So my question is this: Is there any way to get to Portland without having to travel across snow/icy mountain passes? In other words, is it possible to get there without going across big mountains? Is there a path that will be more valleys/less snow/ice? Thanks in advance for any ideas.
 
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