Unfortunately, no. The Horizontal Menu was developed before our concerted effort to provide more styling capabilities in areas like this, and is one of the few components we haven't gotten back around to refreshing or updating.
If the properties in the screenshot are the only settings you want applied, and you aren't setting them through a binding, you could apply them via the stylesheet.css resource (v8.1.22+) by defining a rule which would target the icons of a Horizontal Menu.
div.ia_horizontalMenuComponent__item__icon {
color: #7030A0;
stroke: #000000;
stroke-width: 1.5;
fill: #7030A0;
}
Note that this will apply these rules to all Horizontal Menus in your project and there will no longer be a way to apply these settings dynamically.