Genomes are comprised of contrasting domains of euchromatin and heterochromatin, and transposable elements (TEs) play an important role in defining these genomic regions. Therefore, understanding the forces that control TE abundance can help us understand the chromatin landscape of the genome. What determines the burden of TEs in populations? Some have proposed that drift plays a determining role. In small populations, mildly deleterious TE insertion alleles are allowed to fix, leading to increased copy number. However, it is not clear how the rate of exposure to new TE families, via horizontal transfer (HT), can contribute to broader patterns of genomic TE abundance. Here, using simulation and analytical approaches, we show that when the effects of drift are weak, exposure rate to new TE families via HT can be an important determinant of genomic copy number. If population exposure rate is proportional to population size, larger populations are expected to have a higher rate of exposure to rare HT events. This leads to the counterintuitive prediction that larger populations may carry a higher TE load. We also find that increased rates of recombination can lead to greater probabilities of TE establishment. This work has implications for our understanding of the evolution of chromatin landscapes, genome defense by RNA silencing, and recombination rates.