We investigate, for the first time at z similar to 3, the clustering properties of 189 Type 1 and 157 Type 2 X-ray active galactic nuclei (AGNs) of moderate luminosity (< L-bol > = 10(45.3) erg s(-1)), with photometric or spectroscopic redshifts in the range 2.2 < z < 6.8. These samples are based on Chandra and XMM-Newton data in COSMOS. We find that Type 1 and Type 2 COSMOS AGNs at z similar to 3 inhabit DMHs with typical mass of log M-h = 12.84(-0.11)(+0.10) and 11.73(-0.45)(+0.39) h(-1) M-circle dot, respectively. This result requires a drop in the halo masses of Type 1 and 2 COSMOS AGNs at z similar to 3 compared to z less than or similar to 2 XMM-COSMOS AGNs with similar luminosities. Additionally, we infer that unobscured COSMOS AGNs at z similar to 3 reside in 10 times more massive halos compared to obscured COSMOS AGNs, at the 2.6 sigma level. This result extends to z similar to 3 the results found in COSMOS at z less than or similar to 2, and rules out the picture in which obscuration is purely an orientation effect. A model which assumes that the AGNs activity is triggered by major mergers is quite successful in predicting both the low halo mass of COSMOS AGNs and the typical mass of luminous SDSS quasars at z similar to 3, with the latter inhabiting more massive halos respect to moderate luminosity AGNs. Alternatively we can argue, at least for Type 1 COSMOS AGNs, that they are possibly representative of an early phase of fast (i.e., Eddington limited) BH growth induced by cosmic cold flows or disk instabilities. Given the moderate luminosity, these new fast growing BHs have masses of similar to 10(7-8) M-circle dot at z similar to 3 which might evolve into similar to 10(8.5-9) M-circle dot mass BHs at z = 0. Following our clustering measurements, we argue that this fast BH growth at 3 in AGNs with moderate luminosity occurs in DMHs with typical mass of similar to 6x10(12) h(-1) M-circle dot.