In order to make your document work with LaTeX, you should use:
\documentclass{article}
\usepackage[mongolian,english]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T2A]{fontenc}
%\usepackage{uarial}
\renewcommand{\familydefault}{\sfdefault}
\usepackage{blindtext}
\begin{document}
\blindtext
Монголоор бичье
\end{document}
It will use the default sans serif font, unless you uncomment \usepackage{uarial} (but I do not have it, so it was impossible for me to test it). If it still doesn't work when you set uarial, it means the font does not contain cyrillic characters, and that you should probably use XeLaTeX with an arial font that has a cyrillic set. XeLaTeX allows you to use system fonts directly, using their names.
In that case, you would need:
\documentclass{article}
\usepackage[mongolian,english]{babel}
\usepackage{fontspec}
\setmainfont{Arial Unicode MS}
\usepackage{blindtext}
\begin{document}
\blindtext
Монголоор бичье
\end{document}
Replace \setmainfont{Arial Unicode MS} with another arial font that you have on your system and that includes cyrillic characters.