What part of Utah is going to determine how much extra clothing you will need...
I had family that lived in St. George, and although it got chillier in the winter, heavy coats weren't normally necessary, and a hat and light gloves were sufficient to keep hands and head warm. Now if you are moving to the Salt Lake area, they get snowy winters, so good warm clothes will be necessary.
My advice would be to get into contact with the people you will be interning with, and find out from them what is normally necessary for winter weather there.
Where I live now, (Denver, CO) is fairly mild so far...although I know to expect snow, rain, and nice muddy paddocks! hahaha...But so far everyone I talk to says it can go from a blanket of white one day, and a few days later that will be melted...sooo...pretty mild in my book!
I grew up in MN...now that's COLLLLDD!!!
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."