There is a workaround but you must then specify everything about your ticks.
ticksv[min_, max_] :=
Table[{i, Style[i, 12], {.02, 0}, Thick}, {i, 0, max, 0.2}]
ticksh[min_, max_] :=
Table[{i, Style[i, 12], {.02, 0}, Directive[Red, Thick]}, {i, 0.5,
max, 0.5}]
LogPlot[Exp[-t], {t, 0.0, 2.0}, Ticks -> {ticksh, ticksv}]
to get

Regards,
Neil