I reckon they're separate issues. Assuming that your system is functioning correctly (they won't blow if you've asked for heat and the engine is cold...they start as the engine warms up. Defrost will blow full as soon as it's selected...) - then it's likely your blower fan in need of lube if it works fine when warm...
And you've got a coolant leak.
I don't have experience with either one...so I am sure some more senior folks will pitch in...but lubing the blower is not hard - it's behind the glove box...then chase down that leak. And top off with only the Volvo blue-green...
2006 Corolla (kid's car - 165K, Eco Contacts, Castrol Edge 5W30)
2005 MB S600 (84K, Michelin AS3, M1 0W40)
2002 V70-XC (200K, AltiMax RT43, Pennzoil Ultra 5W30)
2002 V70-T5 (179K, IPD bars, Bilsteins, Conti PureContact, Mobil 1 0W40)
1992 MB 300E (Sportline - 160K, Yokohama Avid, Liqui Moly 5W40)
1990 4-Runner (V6, 4WD, mild lift - 257K, 31" BFG AT KO, Castrol 10W40)
1932 Packard Sedan (straight 8, dual sidemount spares, original paint and interior, Shell Rotella 15W40)