What about the hose freezing outside? Its -10C here now.

I would check for any code violation but your sewer line should be down there and possibly a vent for a future bathroom. You could plumb into the vent or somewhere in the line with a P trap and neck the size down with a hose barb to fit the pump line. I would use a P trap for sure.

"You could plumb into the vent or somewhere in the line with a P trap and neck the size down with a hose barb to fit the pump line."

I believe all of the model plumbing codes require an air gap for drains from HVAC gear.

You cannot plumb the drain line directly into a DWV system.

I don't know how much water you are talking about, but if you have good drainage sand under that slab, they have been putting dry sumps in basements for years. i would make it with sealed top so you don't get any bad smells from it. paulbm

You cannot plumb the drain line directly into a DWV system

Although you should be able to use a washing machine drain box and stick the hose into that.