The loss of most of the 1890 census is one that is lamented by most genealogists and family historians. Many of us have ancestors that are lost in that 20 year gap. Some states have state census in addition to the federal census which can offer a clue of where your ancestors were during these lost years. In other states, researchers must try to piece together the details from other sources.
The Idaho State Historical Society recognized the difficulties that researchers face due to the loss of the 1890 census and decided to do something about it. Using a variety of resources from county records to newspapers to published materials, they have attempted to document the people that lived in the state between 1885 and 1894. This is an amazing resource for those with Idaho roots.
To check it out, scroll to the bottom of the page and look for the link Idaho 1890 reconstructed census file. You will need Adobe Acrobat Reader (available for free) to view the file. It is a large file so may take a while to download depending on your connection speed.
The file is organized alphabetically by name rather than county with one exception. Names from Latah County start on page 1810. One nice thing about it being a PDF file is that it is searchable so you don't have to scroll through pages to find the name you are looking for. The file lists surname, first and middle names, county, record type and remarks. If you find one of your ancestors in the file, you can request a copy of the original record for a fee.
Not all counties are represented in the file as it is an ongoing project, but for the counties that are included, it's a great free genealogy resource for your toolbox.