Any wire outside in conduit must be wet location rated.
Does your planned arrangement include an exterior disconnect that has the required clear working space in front of it (30" wide x 36" deep x ~80" tall)? And does your plan include the required 120V service receptacle located within 25' of the heat pump unit (and at the same level, i.e. not on a deck above)? That receptacle must not be deenergized by shutting off the heat pump disconnect.
With those preliminaries out of the way, the answer to your question is that you can use a wet location rated 10/2 cable method, such as UF cable. While the wires inside are black and white, you may use the white wire for an ungrounded (hot) conductor by taping the exposed insulation another color (commonly red) at each end where you terminate it.
Or if you have a complete conduit run from your supply panel to your exterior disconnect, you can pull individual THWN-2 conductors, which are not allowed to be reidentified in color in the #10 size, so you'd need to get a black, a red and a green.
Note that the supply to your heat pump from the originating panel is two separate segments, one from panel to disconnect, and one from disconnect to heat pump. So the choice of wiring method may differ for each of the two segments. If the supply to the disconnect is never outdoors in conduit, but just enters the backside of a disconnect mounted on the house, that could be a dry location rated cable, such as NM (Romex).
Conversely, the supply from the disconnect to the heat pump is generally individual conductors in flexible conduit (LFNC or LFMC). It would be unusual to put UF cable inside such conduit, as it would require a very large size; and stripping the insulation off a length of UF cable to put the individual wires in the conduit would be a problem, as those individual wires are not labeled.
Cheers, Wayne