I am planning to design a Microsoft Bot Application which runs on multiple channels and bot will be using Adaptive Cards which contains images and other rich cards.
The question is how do we handle or design Bot application which has adaptive cards and support SMS channel or is it by default adaptive cards are rendered and supported in SMS. Also it will be great if someone can point to any samples on it using DotNot Core SDK.
Each bot channel provides client applications that render a UI, and the question of whether or not Adaptive Cards can be rendered depends entirely on the client application. You can see here that SMS is not among the supported platforms, which makes sense because SMS messages don't use cards at all, although there seems to be something called Rich Communication Services in developer preview. However, you can always create your own mobile app that renders Adaptive Cards. There is an Android SDK and an iOS SDK. Your app could communicate with your bot over Direct Line, or you could even make an app that communicates over SMS and renders certain SMS messages as Adaptive Cards.
This may be more difficult than what you want to do, so you might just want to stick with sending images. If you want to learn more about Adaptive Cards, check out my latest blog post.