Arnor split into the three separate kingdoms of Arthedain, Cardolan and Rhudaur in TA 861. The Witch King founded Angmar around 1300, and picked off the three kingdoms one by one. By 1356 he had all but subjugated Rhudaur, which had few Dunedain and was nearest to Angmar. In 1409 'a great host' issued from Angmar and destroyed Cardolan. In 1974 the Witch King himself led another attack in which Arthedain was destroyed. It's also worth noting that the expeditionary force which smashed the Witch King's army was fairly 'small' by Gondor's standards.
So, there weren't that many Dunedain in the North, and they were disunited. The Witch King could call on subtantial numbers of orcs and hillmen. He may also have had support from the orcs of the Misty Mountains; the distance from Angmar to Mount Gundabad is not great.
(Sources are LOTR appendices A & B.)
EDIT (In response to M. A. Golding's comment)
Regarding the last sentence, there is evidence that the Orcs of the Misty Mountains existed long before the Witch King appeared in Angmar in The Disaster of the Gladden Fields (Unfinished Tales).
The Orcs of the Mountains were stiffened and commanded by grim
servants of Barad-Dur.
This to me seems reminiscent of Ugluk leading a band that included mountain orcs in the Two Towers (The Uruk Hai). In addition, the Tale of Years contains the following entry for TA1300:
... Orcs increase in the Misty Mountains and attack the dwarves. The
Here, 'increase' is crucial, because it shows that the orcs were present in the mountains before the Nazgul reappeared.
We can be sure that the Orcs of the Misty Mountains existed before Angmar was founded, and the suggestion that they may have supported the Witch King stands. He may have exerted more control over them than Sauron later did in the War of the Ring, given that Carn Dum was closer to their strongholds than Barad-Dur. However, I can find no mention of Mount Gundabad that predates the War of the Dwarves and Orcs (TA2793-99; see LotR III, appendix A). It does appear that Angmar extended further south than Gundabad on the east side of the mountains.
... when therefore they [the Eotheod] heard of the overthrow of the
Witch-king, they sought more room in the North, and drove away the
remnants of the people of Angmar on the east side of the Mountains.
LotR III, appendix A, The House of Eorl.
The location of the land to which the Eotheod moved is given in Cirion and Eorl part (ii), The Ride of Eorl (Unfinished Tales).
The new land of the Eotheod lay north of Mirkwood, between the Misty
Mountains westward and the Forest River eastward.
However, the status of Mount Gundabad during the time of the North Kingdom, and its relation to Angmar, appear to be unknown.