There appears no direct equivalent of
scroll-conservatively for horizontal scrolling, but customizing
hscroll-step (and perhaps also
hscroll-margin) should produce something at least close to the same behavior. From the manual:
hscroll-margin controls how close point can get to the window's left and right edges before automatic scrolling occurs. It is measured in columns. For example, if the value is 5, then moving point within 5 columns of an edge causes horizontal scrolling away from that edge.
hscroll-step determines how many columns to scroll the window when point gets too close to the edge. Zero, the default value, means to center point horizontally within the window. A positive integer value specifies the number of columns to scroll by. A floating-point number specifies the fraction of the window's width to scroll by.