Do all HVAC units have a drain line

Condensate drip and accumulation are normal, especially during the summer months.

It is also very normal to find the drain lines terminated close to the house as you have described. Whether it is acceptable I guess could be argued based on the volume of water in question and where it is collecting.

If the accumulation of water is getting worrisome, you can buy some small diameter PVC pipe and reroute or extend your existing drain lines. You can even get creative, such as routing them into existing downspout drain lines, or directly burying the condensate drain lines themselves.

If you are worried about exterior-drained condensate freezing, you could bury a standard 4" drainage pipe to redirect your condensate. This pipe could accumulate your condensate via a catch basin, direct piping, or other means. The probability of an entire 4" pipe freezing, especially in the southeastern US, would be approaching zero.

Be sure to maintain a good slope when extending any lines, and drain to daylight any buried lines.

Additionally, you can drain your condensate to some acceptable locations inside your home, such as a plumbing drain (not a plumbing vent stack!).

Use this as a reference:

Cold surfaces accumulate water from the air. For an air conditioner, the indoor unit is the cold one that needs a drain line running somewhere to get rid of accumulated condensate (otherwise the indoor unit will drip water). In the case of a heat pump in heating mode, the outdoor unit will accumulate water, but there is no need to pipe that water anywhere else.

Because mini-splits are often installed away from any convenient drains, pumps are frequently used to send the condensate where needed. Depending on the pump used, the condensate can be moved long distances.

With proper installation the condensate can be disposed of into the sewer or often directly outside. Where condensate is disposed and how the piping must be installed is determined by manufacturer specifications and local building codes. Your suppliers should be familiar with the requirements.