À moins que is introducing an hypothetical fact, so the subjunctive is used.

Quoique is introducing a real fact, but this fact is breaking the logic of the main statement.

This is called a concessive statement. Depending on what conjunction is used, concessive statement require either the subjunctive or the indicative/conditional in French.

Subjunctive (the conjunction clearly introduces a concession):

• Bien qu’il fasse/ait fait/fît/eût fait froid,…

• Encore qu’il fasse/… froid,…

• Quoiqu‘il fasse/… froid,…

• Malgré le fait qu’il fasse/… froid,…

• Sans qu’il fasse froid,…

Indicative/Conditional (the conjunction introduces a softer concession, or no concession at all for the last case, all are more observations) :

• Alors qu’il faisait/fait/fera/ferait/aurait fait/… froid,…

• Alors même qu’il faisait/fait/… froid,…

• Tandis qu’il faisait/fait/… froid,…

• Pendant qu’il faisait/fait/… froid,…

Where there is no concession but a logical cause, the indicative or conditional is expected too:

• Puisqu’il faisait/fait/fera/ferait/… froid,…
• Parce qu’il faisait/fait/fera/ferait/… froid,…

There is also the controversial malgré que which should require the subjunctive but which is more often followed by the indicative in relaxed colloquial spoken French:

• Malgré qu’il fait froid,…