I don't think it is possible to select parts of a TIN, since it consists of nodes rather than surfaces. Maybe someone else can fill in the details or know something I don't.
A workaround that I can think of is to convert the TIN to a shapefile (TIN Triangle) and from that create new layers for specific ranges (Select by attributes -> Create layer from selection).
It is possible to convert to a raster (TIN to raster) and then extract parts of the raster to different grids based on the elevation. That would allow for you to turn off parts of the raster.
Extract by attributes (requires Spatial analyst) can be used to extract parts of a raster based on a specified value ranges. For the SQL statement, use something like
"Value" =< 5
It appears as if decimal handling is a bit tricky, but that might just be me since my general setting is to use comma instead of point as decimal delimiter.
Now just do that for all of the ranges you are interested in to save every one of them to a new raster. After that you can turn them on and off as you please.
Just remember that raster representation differs from a TIN in detail and a few other things. If you need to do any data analysis on your data (other than visual) I would recommend that you stick to the original TIN for that. When you create your raster in TIN to raster, use CELLSIZE XX for the Sampling distance parameter. Replace XX with the (estimated) mean distance between your nodes in the TIN or based on the extent of your data. Typical values range from 2 meters to maybe 10-50 meters, but it depends on what you will use it for.