The Literal Answer
As of 2019, fontspec should find the bold and italic fonts, and load \mathrm, \mathbf and \mathit when you \setmathrm.
If you need additional set-up for \mathit, the ItalicFont and ItalicFeatures options of \setmathrm set up \mathit, just as the Boldfont and BoldFeatures options set up \mathbf.
\documentclass{article}
\usepackage[svgnames]{xcolor}
\usepackage{fontspec}
\usepackage[paperwidth=10cm]{geometry}
\setmainfont{TeX Gyre Schola}
\setmathrm{TeX Gyre Schola}[
ItalicFeatures = {Color = green}]
\begin{document}
Text \textit{italic} (\mathrm{math}) (\mathit{italic})
\end{document}

What You Also Might Have Meant
In practice, someone asking about how to set the \mathit alphabet likely means the alphabet used for $x$.
To set that, you want to load the unicode-math package, set a math font that matches your main font and then, if necessary, add a line such as
\setmathfont[range=it]{Gotham Book Italic}
You can do likewise for up, bfup, bfit and the other math alphabets.
In unicode-math, you would normally use \symit, \symup, etc. for individual letters used as variables, and \mathit, \mathrm, \mathup, etc. for complete words. However, you can give a package option to interpret \mathit as \symit and make migrated code compile correctly.
mathspecis replaced byunicode-math. commands like\setmathrmare very limited. – Leo Liu Feb 14 '11 at 13:55mathastextpackage. – Seamus Feb 14 '11 at 16:47