There are some fundamental differences between MapInfo's styling and ArcGIS's.
Most importantly, MapInfo styles features per-feature in a style string (it's a weird encoding, including a funny representation of RGB in a single int value). ArcGIS styles things in a MapInfo 'thematic', which really means, in categories (that's a over-simplification, as there are other ways to do it, but that's default).
Now, there are some examples where folks have converted MapInfo styles into QGIS styles, which are similar in structure to ArcGIS styles, see: http://nathanw.net/2011/08/08/new-tool-mapinfo-to-qgis-style-converter/. And you can use FME to read and set MapInfo style attributes. I have a couple of custom FME transformers that convert a native MI style into a string that you can store in SQL Server and back again, which is a sort-of similar thing, but still per-feature.
Of course, your real question is about a whole workspace. Short answer is: no. The two packages are far too dissimilar for that to work in any nice way. And, really, there is so much different between them that you'd be missing out on functionality if you could convert them.
So, my recommendation is do it all again. It's not hard to make a workspace or MXD (or a QGIS project) and it gives you an opportunity to rethink things.