[SalesForce] Edit the footer of lightning card

The cards should be in their own layout boxes (instead of being the layout boxes), and should not be floating. Elements that restrict size changes (e.g. slds-size_1-of-3) should be wrapped around whatever it is you're trying to size. Most of the time it doesn't matter, but it helps to get in the habit of doing so, and doing so means using lightning:layoutItem.

Here's a self-contained demonstration using your non-dynamic card example (note: I converted this to an iteration for brevity, it still works "the long way around"):

<aura:application extends="force:slds">
    <aura:attribute name="items" type="Integer[]" default="[1,2,3,4,5,6]" />
    <div>Non Dynamic Cards</div>
        <lightning:layout multipleRows="true">
            <aura:iteration items="{!v.items}" var="item">
        <lightning:layoutItem size="4" padding="around-small">
            <lightning:card >
                <aura:set attribute="title">
                    <lightning:icon iconName="utility:connected_apps" size="small"/>
                    Card {!item}
                </aura:set>
                <aura:set attribute="footer">
                    <lightning:badge label="Tag1"/>
                    <lightning:badge label="Tag2"/>
                    <lightning:badge label="Tag3"/>
                </aura:set>
                Card Body (custom component)
            </lightning:card>
        </lightning:layoutItem>
            </aura:iteration>
    </lightning:layout>
</aura:application>

You will need to use slds-grid and override standard slds css on buttons.

CSS:

.THIS .btnCustomStyle{
    padding-left: 0.5rem!important;
    padding-right: 0.5rem!important;
}
.THIS .btnCustomStyle{
    padding-left: 0.5rem!important;
    padding-right: 0.5rem!important;
}

Your Component:

<article class="slds-card" style="width:31%">
    <!--Header code-->
    <!--Body code-->
    <footer class="slds-card__footer">
        <div class="mybtn slds-grid">
            <button class="slds-col slds-button slds-button_neutral btnCustomStyle">Cancel</button>
            <button class="slds-col slds-button slds-button_brand btnCustomStyle" >Update Asset</button>
            <button class="slds-col slds-button slds-button_brand btnCustomStyle">Update Replacement Asset</button>                
        </div>
    </footer>
</article>