OK a funny question as I am an Aussie and I noticed this about Korea.
In the country areas there will be a tack room to take off riding gear. Your boots will be dusty so ask the host.
In summer we may not have shoes on in our yards so nothing to remove.
In cities follow the host. If there are shoes outside or at the door ask if you should remove them too.
ALWAYS use the door matt to clean your shoes and do this quickly before you knock AND in again when the host answers the door as a polite thing and ask "Would you like me to remove my shoes?"
We NEVER wear slippers like in Korea inside unless it is winter. We never offer guests slippers.
The reason the shoe inside thing differs is due to the environment here. We go in and out many times on our own block of land. We often have outside areas that are very hot or grass ir lawn with "bindies"... awful prickles that attach to your feet and hurt. We have insects and snakes that can kill and we live largely outside. Even our homes open up with big doors to our backyards so the difference between inside and out is not so clear. Our floors in kitchen, living room, entry areas are always tiles, stone, timber to make cleaning easy. We are NOT dirty because we wear shoes inside. In bedrooms we would rarely wear shoes.