  Previous studies showed that an estimate of the likelihood distribution of
the Milky Way halo mass can be derived using the properties of the satellites
similar to the Large and Small Magellanic Clouds (LMC and SMC). However, it
would be straightforward to interpret such an estimate only if the properties
of the Magellanic Clouds (MCs) are fairly typical and are not biased by the
environment. In this study we explore whether the environment of the Milky Way
affects the properties of the SMC and LMC such as their velocities. To test for
the effect of the environment, we compare velocity distributions for MC-sized
subhalos around Milky Way hosts in a sample selected simply by mass and in the
second sample of such halos selected with additional restrictions on the
distance to the nearest cluster and the local galaxy density, designed to mimic
the environment of the Local Group (LG). We find that satellites in halos in
the LG-like environments do have somewhat larger velocities, as compared to the
halos of similar mass in the sample without environmental constraints. We
derive the host halo likelihood distribution for the samples in the LG-like
envirionment and in the control sample and find that the environment does not
significantly affect the derived likelihood. We use the updated properties of
the SMC and LMC to derive the constraint on the MW halo mass $\log{({\rm
M}_{200} /\msol)}=12.06^{+0.31}_{-0.19}$ (90% confidence interval). We also
explore the incidence of close pairs with relative velocities and separations
similar to those of the LMC and SMC and find that such pairs are quite rare
among $\Lambda$CDM halos. Taking into account the close separation of the MCs
in the Busha et al.\ 2011 method results in the shift of the MW halo mass
estimate to smaller masses, with the peak shifting approximately by a factor of
two.[Abridged]
