It's an interesting issue. Although mosquito cell line as like C6/36 could be infected by DENVs in vitro, it's unclear in vivo. Aedes aegypti and albopictus are considered to be vectors for DENVs. A successful infection needs higher titer of DENVs. However, the life cycle of mosquitoes is too short for DENVs replication. It's controversial that these mosquitoes are only act as vectors, not reservoir. By geographical analysis, in subtropical area (e.g. Taiwan), infected cases are only found in late spring, summer, fall, or early winter. In addition, epidemiology shows different serotypes outbreak in next year. Due to these reasons, in my opinion, it's unlikely to transmit by offspring. The following are two references for you.
Lee H.L and Rohani, A. 2005. Transovarial Transmission of Dengue Virus in Aedes aegypti and Aedes albopictus in Relation to Dengue Outbreak in an Urban Area in Malaysia. Dengue Bulletin 29: 106-111.
Additional studies are urgently needed. However, I believe that TOT exists for all arboviruses. For some to a lesser extent (such as DENV) for others more frequently (such as RVFV).
There is not a report/study about how the dengue virus survives the winter; however, it is quite possible that the virus hibernates in the eggs of aegypti. Examining the winter ecology of the dengue virus would be a very nice survey in endemic areas where the winter is well expressed. If the virus is transmitted vertically through the eggs, why not to think that the virus is in the eggs in winter?