We present the Spitzer IRS spectra for 33 young stars in Tr 37 and NGC 7160. The sample includes the high- and intermediate-mass stars with MIPS 24 μm excess, the only known active accretor in the 12 Myr old cluster NGC 7160, and 19 low-mass stars with disks in the 4 Myr old cluster Tr 37. We examine the 10 μm silicate feature, present in the whole sample of low-mass stars and in three of the high- and intermediate-mass targets, and we find that PAH emission is detectable only in the Herbig Be star. We analyze the composition and size of the warm photospheric silicate grains by fitting the 10 μm silicate feature and study the possible correlations between the silicate characteristics and the stellar and disk properties (age, SED slope, accretion rate, and spectral type). We find indications of dust settling with age and of the effect of turbulent enrichment of the disk atmosphere with large grains. Crystalline grains are only small contributors to the total silicate mass in all disks and do not seem to correlate with any other property, except maybe binarity. We also observe that spectra with very weak silicate emission are at least 3 times more frequent among M stars than among earlier spectral types, which may be evidence of inner disk evolution. Finally, we find that five of the high- and intermediate-mass stars have SEDs and IRS spectra consistent with debris disk models involving planet formation, which could indicate debris disk formation at ages as early as 4 Myr.